{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rotating Bar\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/grids/Rotating_Bar.ipynb)\n",
    "\n",
    "This example simulates fluid flow around a rotating bar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install --quiet phiflow\n",
    "from phi.jax.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well.\n",
    "from tqdm.notebook import trange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by defining the rotating bar in its initial orientation as well as the initial velocity field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7Hhb4bm62IKmo5kHPCelGWpf8YL+LxcC8efnRcnJu12omZJuPljMu3x7B5Y31JqQ+lT9Ny6eb6WLynd0OJB4Vl7Yfocb78WEf9fvvSVxOAy90JB3GDGlaEDGkMmLMOaeYcSoVCxTFjIoFgwzDUNrKnxczTgYlaVeerRgzxolTkn6PspX9GeW77M84vovxaX3XXD6/XJ7En2eRy4jxsf0ZxeVpMSySfqFv0hoaGhrnAVruyMFHy7Whrcw1qZV5nLZwkZrd38tamfPawkUKddK2cCG/jNMWnrUyt7H6Pk5buKj0eHuMtvB7Ulv40FbmftbKfNK28E2plVnVFp61MpuQX/LawsX4QGpl/nxteCtzx85amU/aFi6krLy28LdO2xa+Pn5buJDWRrWFhzGjnzyopFxmbeHvL9VQsZHXFi42xr++3kR1UF5b+McriRx00rZwIWW9u3iobAt/S2oLv3PKtnAhC+a1hb8vtYULKUu3hQ+BjqQ1NDSeB+hIOgfyr1/eWERuch3kqPcxxhEVjLLlnKNedRzbk/gj247rD2Mn82dc26P+jLI9r1yexB/N5bPH5Un8UdlOAy/0Tfr6RgvVHT97VMPrYlzvZ6vWd3Y7qO6Qbd9NZYK+F6J9dOmwT7tpSvzB4xomgXhfEDH6KK0A2GjYtJquWn+61oDcIWw55/RemmJVeh6esXZzK6tIED7I444doE32wX6XKmlK/N5SDZNLHMMLY/o03TFvtW7i6dIfLdchdwhbxjhSvr22i5baGxstSEeyP+DS9PD8vDu7WUWCinfTC+m6xKVoT/7gcR1cimOEMaMPUy43mzatpFLNZ2tNyB2yP4LLw55H91Muv9pqoyJB5U/HDtBO/uCgh+oOmUtxDC+MIY2s1S3aTJ8ufW2lAblDxeV+x0Xr+RebLcgdqrnWMH3IXvf21FwKW8uP6PM0nX9c7dO2xKW4uYj3hTGjDx4nXG41bWyJ8Nl6xqWKn2rfg+z19XYb0pFqHvScEFw+POhhC4L3c+blxysJl+sNC1LNxysNyB3iGHlcfrnZRnWHyp+mlVXKJFwmvot5Ir/P9iP6LOVyuWqCyw+X61O9UWu5Q0NDQ+OMoeWOHOy1HexkJRb65LEbxIhSqj0PUa7KNowZaj6blo+oclthyzlH7W/PCVHvvNtyECmqjmH7EaL5StdFNKGy9aMYiyB108PCj8o2ZhyLYR07QOSx07KRNsrvE9/J9EJETfud0VyKBa5afzSXwp/WCbkU2cVe20F0k8tlem4Peyfj0hrBpVgM69gBFq3G4VIsuO13HGQwqmN44SCXIspV2UZHuBQR+nbTRuQqcyn86bnjc+kEJ+NSZCIN0x/KJZO47DoZl7stR8nlloLLg647kkuxh3T9BFy27UDJ5TTwQt+kXWlrQiF7yOOQMdxM3DCmkLFc25hxclJbP2IUphPD8iNMKNlWTE4/jskXWzAGkdIfy8u2j/QCNpbvUSz5E2bbj1petnWj0p8o26LS8iM8fVvYMsk2iNjAFpUjuZRsg3g4l8LWk7aoVHHJOB3hMs645PlcRjEnL0w+1wliPBl75LkNpXOr4JJxTnZ6oQexvL1mfIxLzjMuw5jD95Fcxgw3Ey+MKYyHzIOj8zKWuOSDtjKX8rl1gljJJfyJ+MC5HcWlK/keDOEy5kfnZeb7UX8459I2q/LWqRFFQ67bSNqq1A1jCiMOf475zjMuB3yXuJwGtNyhoaGhccbQckcObm628Est6nKJCPXODdPH/rH397pI7cXf5feZXoha0ZWqCenj45VssUvYBhHDo612WjbqLW+sNxEBiGNwzjGu9jzUrt7e6SD9k30X454TYqHuUaWH9Pjach0Ri7D1whh1txsNCynvZ2sNRAvCljFO19I61/2Ogzrgr7baiDhUXDYtH4tLD/a7SEdVXFp+hFbd1ZqJFFPFZRgz1IPvtpyMy40mIiTZH9GyXetnXN7Z7UByyucyObdLlT7S4zwuRd3tZsNCqvz5WhORsorLg66LOuCvt9uQeFT+tCQuH+73hnJp+xEW6o5yKSQM8b4wZlj0TLhMzu0XGy1E7qpzW5e4vLvbgUyi5NINsei5VOlDRsrjUmy1cJRLcZ2ouKx0XbS039puQ5ZQ+d62A9SnP9zvQbZRcekEEfom1usZl5+sNqZb4cE5f2b/+/73v8+fBKYXcsYY55zzvhvgdTGOYsZtP+Scc277IY/ifFvGGDe9xNYNIh5Eca6tPPbDmHthNJZtGMXc8RNbywt5PMSfOGbckvwJx/THCyPuh+PZBlHM3SDxR3Op5nJcf07LpeNHQ7kUnyd8H/fc+uGgP8NsZS5tfziXjA1yOe65PS2X1ggu4wlzeVoQ0S2ec5/TcoeGhobGGUPLHTnQbeG6LZxIt4XrtnDdFj416EhaQ0PjeYCOpDU0NDSeUbzQN+mPlmuoSMiTO8TK+Dhyh6gcuL/XRYVEntzxzinlDlFlMI7cISpIbu+0UW0yjtwhnuP2zhhyx31J7hgmHdUl6eikcoeQjvLkDiEdrdczLvPkDpESH3RdSEefrzXRFp4nd3x6SrljtTZc7vjxaeWOjfHlDsHlKLkjGpCOMrnjg6XaUOmoIklH19eHS0ddJ5OOTip3COno3cWqUu74sSR33D2l3CEqd/Lkjg8kuUNwqeWOIdByh4aGxvMALXfkoGH6iMxE+7c89qMY9bMdO0BUqbKNGUcE0fdCRMQqWyJCVG77EaL5uukhmlC9zwtjtGy3LB/dYyrbKGaIDntOiMhDZcs5R7u56YVYJKrn+C7GbhAj4mtaw7kMIjbApYgq87gUi08n4dIJBrlkQ/zxwhgRVtsOpsKl5UdT41JkUV1nOJfsCJciIs7jsvYUuBTXSc8dg8t+xqUlcTnyOpG4jIb4c1Iu5etExeU08ELfpA97Lk7KZkOxJ4EfUz2d4DVp/wvZVoy9MNvfoWUFSP13pP04hG0YM9pL5YeuG1LHTmwPOi5aX+X9FMTY8iNqWOleIn0Prbgqf5wwpmo6eRqWR6aX7UkgJriw9SNGB+luZF0npG46wfek/TiELWMcu9L1vWx/h8OuhwtO6U8QUS2d4HXTJ8c/vr9D5k+2n0LbyvZI2G2ruRQ7DnadQS6DI77Lx7P8CDevas9Du6/KdzeM6bAnuPTB5baCyyBm2NmtYwfUSW9ee51sDwkVl6YX4ofgsDvi3AYRbgx10yd7KJcM8zKPS9XeFPLeHZWuN5RL+yiXfr7vXsQgzxzd40bF5Z7EZVfiUrTC581L8UNQ7XnkRfm+y/vz1E0f7eD5XCa28t4d8t4m04CWOzQ0NDTOGFruyMG9vS6iY1F3Ko/bdoD20seHfaTrKlvbj1AzvNmwEC18udlCxCJsw5hhoWW/42AXt9s7HUSjwpZzjkWihuljUW/xoIdfcpU/fS/Ews9azUSadmOjiYhF2HphjAXJ3ZaDRcavt9uI/oRtzDgWU6s9D4sn90dw2bEDWqpkXLaHcOkEg1yKqPpmDpeiRveg6w7lUnx/oiSKW5W5dIZzKZ4+vV7PuPxiozWSSxGZqrhkjGMxtdb3UHd7f6+L1F7lT9fJuFyu9hGBq2zdIMYi2lbTRlR9c7OF6E/YRjFDO/5B18Xi953dDiQn1TGalo9FvUeV4VyaXog90dfrJuQMFZd+FGNxd6+dcXlru40MWMVlXeLywX4Xsk0el2KxeaVqIgIX8+Qol6L+ejuHy6kgrxXxWfjvSdvCm6aHFtZa38XrYuyHMe/aSctn1w7QBqqyjWPGm6bHOU/aREVbqsqWc87r/cTW9kO0yTZMDy2s4u/y+7ww4l0n8adt+WhPVh0jjGLetvzEdydAS63KljHGG6nvlheiTVblgzx2gwgtsS3LR0utyjaIYt6x/SfiMs8f8brjR2jblblU2Z6Wy96Ic3tSLsXrbhDx3pS5NL0Q7duyP6rxOFyq5mXH9tHqrbKNYsZbY3Ip+3PSeTmKS/EZR7kU14nqGHGcnds8Lk8L0m3hGhoaGucXWu7Iga6T1nXSRLpOWtdJ6zrpqUFH0hoaGs8DdCStoaGh8Yzihb5J613w1HKH3gVv0Fbvgqd3wSPSu+CdClru0NDQeB6g5Y4c9L0Qv94icpHHUcwQQdh+9pBYlS3nHFG5G2QPqVTZymM/ihEVjLKVH0AqP5RVZSs/MNYJInQOjjqGF2YPcx1lG0TZg3pHcRkzPsBlNMQfmUv5gZ/T5HLYuWWMY4H5pFyO64/MpTkGl9YpuRz33Mpcivfn2Uan5NIN4qlwGcaDXA67TibN5TTwQt+kV6om2enJFOmRPO66IVpCNxoW0qYB2/Q5gnYQI7Xd6zjUSNPn+3tdTFrxviBiSCVrPR+PuF+q9DERhS3nHOO2HdB2M0kP12om2pOFD/LY9CLIFttNB9LI3d0ObgDic70wRnNEpesifV486OEGKWxjxiFxNCwf7e2rVROTfcAfwaUTINXebNhoPVfxbgcxLR+mXLYdNI8McJkeI4wZGk3q/YzLx4d9XKiyP0JS6NgBJKmEy3x/Ei4T33daDrUsBZc7GZdCvjrseeDy0UEPF7X4XCZx2bR8tLev1iQuFXOt54a0kabaW02bOo7C99TWkbjc7zhU7yfz8sF+Fzck8b4wZmg0qfd9tLc/rvRxE1bx03YCXCfrdYv64twq5oHpS1y2bchM9/a6ynn56GAElztqLnfadsZlkD8ve24I2WKraVN7yDXuhjE9Tq+T/Y6r5HIa0HKHhoaGxhlDyx05WK5mkevd3ePRVs8NsWi12bCQ1qhs3SDGwsZe20GE8GC/i3RL2EaxFEn3PSxWPKpkEYKICjjPIoSOHaDteb2eRVsqf2w/Qr3zTstGS7scsdyVInsR/VW6LjacWTzoIUK4K0V/ItpqWj4W0VaqJiJXlT99L5Qi6eFcemHG5X7HwUJUHpdZJJ1xuVTpg0v5GILLrhOglv0kXO62sqzk/gguD3uDXIYKLkWdeeuUXG41bbRhi+92lEuxtcF+J8tKHuxnWYl4X8x4xqXpDWQlqutEzaWFrETluxNkGd5uy0F9uorLULpOqlIkreKSczWXqzUTWYDKd9MbjKRFtjyKy4OuCy4f7vfA5TRQmtonPwO4PFemUsEgIqJXLszidTGeLRXo4mxC0cXZEs2WCrm2paJBl+fKRER0YbZE5WLyuVfnZ6hw5BjFgkFX5hPbuXIRk/PKfJlKheQYLy/MEBGRYRgYz5YLtMCEP2UcI8+fS5I/s+Xscw1j8H0lyZ+FmSL+fmW+TMUjvhcKBl2dn4HvhdT20lyJSkP8mSkW6JLgcm4El4XM94WZjMuXFtRcXl1IuZwp4iZ+eb4ELuVjCC5nSgW6MDsel+VigS7OJbYLs0X4/lIOl2IeLJRLRMmf03N7nMuXcG6LOO5JuLwwW6SZ0uCcOebP/HEur87P4NyK9xUMyrgsF6lcEFyWqVzM53K2VKQLsxy+q2wzfwp0SeJyLv3eKi6LRjYv5yV+rsyXqXjE1jAyLueOcjlkHpSLmT8XZos0WyqOx2W5SEXB5UKZUiqngjOROwzD+NtE9DeJiBPRQyL6d4joDSL650T0ChHdJqK/zjkPhn2Oljs0NDSeB5wrucMwjG8T0X9ARD/gnP8yERWJ6K8S0d8non/IOf8FIuoQ0e9M25ePV+pIzUTtrzyu9T3Uf97czOqkVbZ9L0T958P9HmSJtx8eIhUStkHEUEu7XjeRQn2wVEOaK2w556hdPei6WNC4sd5E2q3yp2MHqP+8s9tBW/hPHmT1qMLWC2PU0j4+7NN6PWu/FQuHwjZmHDXeOy0b0scnqw2sfKv8qZsedlj7aqsNGUBla3ohXUu5XDzoIZV+R8FlGDPU0q7XLSyAfvg4a2WWjyG4rHRdur2TcSnS7jwuP19LuLwrcfnTB4dKLkUt7UrVhEzys0dVyC/CljGOGu/dloN0/dPVBuQglT8N08d2BV9vtyEDqGwtPxrgUsh37zzMantVXG40LMg2Hy2ruRTjw56L7QpubGQ15yrbrpNtV3BvrwtZIo/L99L6/dWaCZnkvUdZW7iKy712xuVnaw3IQSp/mpaPXohb21lbuJgnsq3tR+iFeFTJuHx38Tmrk05v0l8S0Z8moj4R/Y9E9P8kon9KRK9zziPDMH6NiP4e5/wvDPusJ42kY8aR8uWNGeNUKBj4/zjvE5wahjFR25P68zR9P2/+PItcck7nyp+nwaVhTN6fs+TytDhXkTTn/ICI/nMi2iWiQyLqUSJvdDnnUWq2T0TfVr3fMIwfGoZxyzCMW41G44l8kYnNG4uTVhjDVowNw4C+Nknbk/rzNH0/b/6MzWUcPrnvcTgR38/ruZ3mvJyGP2fJ5TRwFnLHS0T0W0T0c0T0LSK6QES/Me77Oec/4pz/gHP+g9dee+2JfNFt4botnIplor935cn+K5Z1W7huC6dp4Szkjr9MRL/BOf+d9N9/g4h+jYj+Mj1luUNDg4iSG+0Tvb83GT80XlicK7mDEpnjVw3DWDCSfOHfIKIlIrpGRH8ptfltIvrjaTsiIpu8MecckWQQMfzSj3pfFDOUgo2yjRnHr/AoW8Y46kNH+SP7Hp7AnyhmiFbH8Wdc35+Ey3H9OS2Xk8AkuAxPwWUYny8uT3JuTzIvY8afCpdPep1MA2ehSd8kon9JRHcoKb8rENGPiOg/IaL/yDCMdUrK8P5w2r58vdVBdYfYsF8eNyyfHqYp38ODLlq9VbamF9Kt7STFWqmZaAT4ZKWBkylsg4ghxdpp2bSZSiNfbLQgdwhbzjldW05ki2rfQ/XC3d0OdZ1837tOiPT58WEfTw6/ttzARSRsvTCGrLPZtGk7rUy5vt7EBBa2MeP0yUriz0HXpZVUGrm93YF0pPKnaQX08KCbctlDSpzH5ddbie+rNQtPMv90tXmMyzBmqLzYbTu0kbYnf7nZhtwxeIzE95rp0aOUy0lA5vJGyuVW04bsdX29iYtZ2LKjXFYzLoXcoeKnZQeoqhnFpe1HkCLW6hYqUz5dbeImLHP52WrG5XoqjdwcwWXd9CGN3N/vQoZT+dNzQrqzk/i+fGhSJa2m+HhFPS9vrAsuLXB5Y70FuUPm8uOUy0pP4nKng+oOlT9tO6D7KZeLBz3pGm8cs7X9iG5uJlyuNyxIiJ9JXE4Dui1cQ0PLHRpnjPMmd5wbbDdtRIpisUwe236EiHi/42DxRGXrRzFqo+t9D7/eazUTEYKwZYxj0aFtB6gr3WxY+EWWjyFqbfteiDrOvbaDaELljxfG+KU/7LmIctcUtlHMsDjXtHxEQut1C+mfsOWc4zN6TojF1J2WjUgxj0sRxR103aFcBhFDbXS972HhZ70+nMuOHSCq3GxYSHlVXJoSl5PAOFzGw7h0Q9SOj+LSCTIuK10XLe0juTTH4TIZy1xuNW0ll6sSl2LBba/tIBvMm5disbDa85AxqOZlzDgWOluWj1r2jcZxLuXPkLncbQ2/TpwgwnUic6nyJ4wZovmjXIrrZBp4oW/SMefE0okaxRnJYsw4B/mcJ+2RebacE0VMvI/wuTFX2FL2d/kYMePqY0g+iLkQs+G+c06YyIwn/5Y/66g/sJU+l3G1P7H0dzGOGc+OofKHiFiaEbJRvhOXjpF950hxjAHf06crZ+N8LpnEzyQwwI/kj8o39bnNOBnJJc+4TGyHc6maPyouk88j+Du2P3RkPg/xh2hw/sB3xffgA/wNzn2VrcyleJ/q+jvGpfQ9meSPyjZmx8dTVDqISMsdGhpa7tA4c2i5Iwc31ptYOBR1wkSEVtS66aHe8s5uB+nfe5KteJ/phagDXqr0kUJ9sFTDL66wDSKGVt2tpo3U6tPVBlJFcQzOOcaHPRe7lH293cbOdj9T+NN1AiwYPdzvIbV/71EVUYiw9cIYNdVrNRPp+rWVOuQgYRszjrrbvbaDhcwvNlqQVFRcNkwfXN7d7WAHMRWXlh+hDvjxYcblh4+PcxnGDAs7200bqelnaw0sdsn+iDrXas/D4tskoOJyvW4iXf94pQ4JQ9gyicv9joN6+Twuxbhp+Whpv7fXheSk4tKWuFyu9iE1fPi4BmntPYlLUeu/3bSx+Pb5WlPJpXhfre+hDfv2ThuyhMr3nhNie4DFgx7kxPeXasp5+Qm4tMDlJ6sNSBgqLg+6LhYyv9xsQXpU+d6yfLS039vrQibJ41IsUq9UTcibHy1nXE4DL3Qk7QYxzc8Uc8eMcQpiRnPlInlhTDPFAhUKRu77vDCmuXKRgohRwSAqFQsjjxHFjDglu3GNso0Zp4gxmi0l/syWCmQYan845+RHie9+FFOpUKDiEN/FOIwZGTSe76IsaqZUwHefFJdi/DS4nEQkncclncCf03DpRzGVC9PhkvFkt8BxrpPwKczL03I5zJ9Jc3laDIukX+ibtIYGEWm5Q+PMoeWOHHy0XIPckdcWLnYbG6ctXKTd9/e6WFHPawt/55Rt4SI1G6ctXOw2dnunjWqAcdrChfzyzhht4feltvBhLfZ1qcX+pG3hYkU9ry1ctNiv1zMu89rCRevwQddFi/0kkNcWvipxqWoL//Fp28I3xm8LF1yOaguPBlrss7bwD5ZqQ1vsK9KT16+vD3/yetfJnrx+0rZwIb+8u1hVtoX/WGoLv3vKtnAhC+a1hX8gtYULLp+7tvBJQkfSGhOBjqQ1zhg6ktbQ0NB4RvFC36TH2QXvacgdokLivRPIHZ+vNc9E7oifktwhqgxOK3e8n5OiPw25Q3Apyx3vLo6WO7Cj4BnJHeEQuWPULnjTkzsSLqcpd9zQcsf0oOUOjYlAyx0aZwwtd+Sg2vPwCygiTXnshTGigobp49dbZRvFDBFN1wkQeahsOeeoDzW9EFFTpeui+1D1PjeIET3XTQ9Rrso2iBgi/7YdIEJX2TLG0dbbc0Msph50XUQ3qvfZfoRa7Vp/NJeizrxpnY5LwdlQLtOa2MPeaC5FPe8kkMdlfwpc+tH4XMaMD3BpDZmXwk+i41zGQ7j0wozLuukhY1DZhvHgvBTZTt51IrjsexmXlRFcOsEgl+EILkXN/jhciki754TgUp6X08ALfZNu2T6FacunmMhEhIJ2P2RIlXpuQH7IBv4uvy+IGbXsZKL23YjsdPLVTR83C2EbM07N9CKz/Rg3xZYVUMgGj8E5x9gJIvjTsUNcDLLvsj+d9CLruSEuhlrfwwQXtiFj1LKSzzW9bPI1TR/tscKWMU514XsQ4cJpWQEF6cWg8kfmsusEuBhUXIYxH+Qy9afe93CzkLlsyFz6w/0Rx3PDGD+Ok4DMpfhht/zM91FcOkE8NpfeAJfhCC4zf0wvIif1p2H64FK8L5JuoEf9CYdxGcTUTbnsOiH5Ub7vQcSold5A+25ITiB894/Py5hnXHoRWV7KpXX8umWMU62fcSnObdsOEMwor/GIYTfJnhsimMnjUlwnfS8cmJda7siBljs0JgItd2icMbTckYPbOx38GopWXnncsrJ9chcPekjpVLaWH6FVd71uIk27vp7tgSxsg4hhEW2v7WBh7KutNqIiYcs5xwJgve/hEUL397pIR1X+9NwQi3rL1T4ipM/Wsn17ha0Xxmgh32raaMP+YqOFKETYxoyjrvSw52LXtNs7HUTgKn/adgAuH1WGc2n7ERZI1+sWuLyh4DKMGRbR9toOWtq/3m4jKpKPAS5ND09pnwRkLkXb83bTxsLYl5stZD7CljGONuPDnosF2zu72T7nKn46R7hsDuHSCQa5PJC4FNGfsI1ihkW0/U7G5a0cLsW4YfpY/H6430OUr7Lte9k+56s1E1Hq52vNY/PSj2Is3O+0bLRhj+Ky2vOwYHt3N9vnPI9LsdXCUqWPrEzMk6NcisXmjUa2N/eNDb2fdC6eNJLuOSFdni+RYRjUsQN66cIMERHGYczIC2O6NFcm0wtpvlykUrGgtGWMk+lFdGWhTE4QUbFg0GypqLSVx14YE+dE8zNF6joBXV3Itw0iRkHM6OJsifpeSBdmSlQsqH2PGSfLj+jKfJksP6KZYoFmSmrfiQjHdoOYDINorjzadz+KKWacFmZK1HNCujRXokKOP1HMyJW4nCsXqZzDJeec+u6Tc3llvjz03PpRwuUkIulJcBnFnC7MlqjnhnRpdjiXThjT5VNwWTCMsfw5LZej5iVjnMx0Xtp+ROUR81L2h2g8LoOIURizqXDZc0O6ujCTy+VpodvCNTSGQcsdGmcMLXfkQLeF67bwSUG3heu28GlBR9IaGjqS1jhj6EhaQ0ND4xnFC32THqctXKTo48gdopX5/l6WoufJHW+fUu4QKfo4codYlb6900bFxjhyh0jR3x5D7rgnyR1DU/R+lqKfVO7YlFJ0ldyRpegmUvQ8uUOMD6QUfRLIkztEip4nd7x1WrljfXy5Q6To47SF/+RB4o8sd7w/Rlu4qA66vt5EhUSe3PFx+sCLk8odorLp3cVDpdzxliR33Dml3CEqifLkjvcluUM8W1PLHUOg5Q6NiUDLHRpnDC135KDrBOgGFFGpPA5jhki774XoulLZMsbxi237EX7pVbby2AtjRHydEbZBxLDQ2XNDRJUq25hxRGOWHyEizvNHHNsJxvfdj2JEWKO4jM6ASxGAjOJyElBx6QbxqbjsOeHYXJojuOT86XLZc0NElbnz0snmpcguRvnjBjGyzHG4tCQuh10nUcxwnYzD5ajrZBp4oW/Sm02b3JRoITnI474bQibYaztkpm2pKlsnjGkzlTgOex510gtj+bCPSSJsw5hBUmiYPtXTdtb1hoUTL2w552gU6LoBVbpJarvTsjERVf5YfoTi/4OOiwt1qdLHBSdsvTCm9TQNrvd9pKurNRM3d2HLGKfltAmkbQdYDd9s2uQM49KLkNrutR3qpxeGytYNY9poZFyKi2C5quZSSApNy0dr8EbDIi9kx44huOy54UT3XJC5XEvT4Lrpgcu1HC5FQ03HDpFqbzYtbCug4scc4NLFTWYUl9W+h5bs5WofN1NhGx3hUsgom83RXO533NQfZ+i8tIOIttJ5Wem6aMl+fHh8XvpRDEmhYWbzcr1u4eau4rLrhHSYcrnVsodyafkRrvH9Tsal+G6yrRcy2mwm/lR7GZcrVVPLHXnQcofGRKDlDo0zhpY7crB40ENKJy8iiXHXCVAzvFYzkaapbJ0gwkLLTsvGIuPtnQ6iP2EbxgyLRIc9F7/kD/a7iKSFLecci4Uty8fCz3K1jxRT5Y/phVho2WxYaMO+td1GxCJs/SjGk7P3Ow6i47u7HaR/wpYxjvb3uukhWn9UGc5lzwnB5XrdRGSvsnWDGFzutpyhXEYSl9WeBy4f7veOcSm+P1GSBQguJwGZS1E7ftB1ER3f2+sikh7kMhnXTQ+19Y8qPUgfSi7dEJnYet1ECq6y9cJBLsXGQXd21VzeOSWXIuJdqZqIRlX+WH6EKHWraSM6vr1zfF4GEcPC9EHXReZzfwSXDdPHwv1SpY/IPo9LkT2s1y1weSuHS9FCvtce5HKakXRpap/8DOAbl2aTp0UT0bevzuN1MZ4rF+nltN3z5QszNDdTyLWdKRboG5dmiYjo6vwMlUsGERG9cWWOigVjwLZUMOj1K3NERHRprkwsnZzfuDRHM8XBYxiGQd9KxwszJSoYyWe9cmEWT5TO8/2VC4k/Ly3M4GnG37o6T4Yx6E+5UKBvXEr8uTxfJiP9rNevzFHpiO+FgkFvpL5fnC3RbDH53Ncuzh7zfcCfmQK4fGlhZqjvM6UCvZZyeWW+TKXiEC6LBXB5ca6EG89rl9T+ZFwWiejJWnllyPPgm5fFuS2By29enqVyUcVlMr44W4K/r12cpdnSEC7Lg1yKc6uyLRfVXL5+OYfLy8e5/Mbl8bl85eIMzQ85t7OlAr16KbG9Ol/GPHjjimJeFg365uXE98tz2a3qG2NwKf7+6qWZkVy+cjG7xuXrRMXlN4Q/82VcG69fnqNScXrxrpY7NDS03KFxxtByRw50nbSuk54UdJ20rpOeFnQkraGhI2mNM4aOpDU0NDSeUbzQN2m9C57eBW9S0Lvg6V3wpgUtd2hoaLlD44yh5Y4ciKiViBApyGPGOH6xvTBGq67KVv685CkbbKitGIcxQ7Q6yjY+4o/4gVXZcj5oG4/wXYzFUy3GsY1ihuhwWlwGEZs6l5PApLkcdm7PM5ej/OGcD1wn487LMH46XJ7kOlFxOQ280Dfpe3tdyB3X11t4XYxbdoBW08eHfbSBqmxNL0Slw2bDpsM0Bf1ys4UTL2yDiGE1fL/j0m47Sefv7HQxgYUt55xupOO66WFFefGgh5RY5U/PDZGurtctPLb+xnoLk1bYemFMd3YS33fbNlp8v9pq40IVtjHjkIAOex5tpi3H9/eHc9l2Mi6XqyY106eBq2wtP6K7e0m6utm0wOXNzfYxLsM447LSddFcc3f3OJfi+xMlbc9rtck1s8hcimaf3baDqpqvtzu4cQhbxjgkoGrfo4164vuD/S6ZaTWFip+OE9BSyuXKCC5ticutpo1tBW5utnGTEbZRzOimxOV2yuW93S5uRKpjNC0fss6jSh9PDlfZ9r2IHkrzsppKiF9sqOflre2My92Uy1vbHdxYVVzWTB/XyYP9LvW94Vw+SptrVmsmmr5u5HB5b7dLRETbLYnLrbaWO/Kg5Q6NiUDLHRpnDC135GC9fnxDI3lseiEWNnZbDiJF2VZEq16YbQZz2HOxqLdU6SP9E++LGUfNZ8P00V66WjOR0qn86TkhFgC3mjaiG+GDPHaCCAtu+x0HLe2qz5U3fKr3s02BVBsayRs+dewAdaUyl7I/qg2f8rgc2PApfQq5zOXjw4xLcQyZy2SDpYRLeUMjlT89afOsSUAcI49LeROeUVxuKDbako8hc7nXdrBgq7JNNilK/Kn2PESKMpfyvBTZjrzB0nr9+OZQ8ljmcrtpo6ZaxbsbxKh7P+gO3/hL3vCpbnrIBmUuxTEGNiJzArSQbzQsZFQqf2w/wiL/OFyKRfU8LqeBF7otvFw00GYtWkflccEw0EZbLBpoo5Vt58qZrWidLRYy25lSgdJD4H0GJS2mREmLeMyFPwW0ESv9KRCVCtn7hO/Ch6P+iLbVUqFA6duUnyv7UygYVEw/N8+fmVJmK/iZKWbfU/Yn45LQOlsag/eyzKXsz5FjyL4XDQNhR6lYoMIQf4qF7BiTgMy77LsB37MxeDeMQS5Th8uF43Nm8BgZlzI/efOyrJiXMpfyPBD+lAoGiSS7lOOPzKWYB/K5VfFuGINzv4DrRM2PaO8uGmouMQ+OcFkujDsv1b6fhEv5Gp8GtNyhoaHlDo0zhpY7cvDZWgNpt6hblsf1voe65FvbbaRbKtu+F9Lna0m95eJBDzLJzx5VIRkI2yBiqLfcaFhI6a6t1JGaCVvOOWpFK10Xi5NfbrawY5fKn44dYCHl/l4XqfS7i4dIK4WtF8Z0LW3VXamaqP/8YKmGNFfYMsZRU73bcpAKfr7WRKqo8qdh+qhLvr3TRs25ytb0QtR4P6r0kNq/p+AyjBladTcbFqSPj1fqkIPkYwguD3suamkngQEu03r5tZoJCezDxzUsHMpciprqvXbG5fX1JhaF87j8Glx2IPGobC0/wvYAS5U+Uvv3HlUhGai43GrakD4+WW0ouRTjas8Dl19ttSEDqGx7ToiW9gf7Xch37y5WlfNSbLWQcJlcJx8t1yAHqbjc7zjYre7GehNSn8qfpuVj4fnObgcSj5gnsq3tR6jxfnzYh5z4/lJNLxzm4Ukj6SBiSJFUY845RYxTuVigMGZUStPXUe+LYkYFI0nlRtmKm05xDFvGODHOqZT6I1Kv8+DPs8Yl55xilvg+iUj6eeOSMU78BFyep3P7NLiMGSeD6Jjvp8WwSPqFvklraBCRljs0zhxa7siBbgvXbeGTgm4L123h04KOpDU0dCStccbQkXQOYqm2cdT4JLaMcUQFo2w556ixnKTtaf2Zlu/y+LxxOQm8yFyKz562P9Pmkk3A92nghb5JD1R3yKu5i3J1R5I23d7pZBUJCtu+F9Lnadr0qNJHC+tARcKiVN3xWFR32LSSpsQfy9Udi3J1R5I+V3oe3UufRXhzswW5Q+VPxw7oZirV3N/vUgWr1tIq+mK2ii42Yl+tS9Udj6XqjsVsFf09Ud3RdtBSe31dqu5QcWl6kBfu7EoVCQpbubpj6bBPO2lK/P7ScS4HqjuaGZefrErVHdIxBJeHPY/uplLNJCBzieqOuqWu7pC4FDLTXtulxYqiukPBj1wpc3cEl5Yf0acSl9sSl6juyOFyOZUXPpWrOxTHOOy5aD3/aqsNuUNl23NCyF4PDnrYguBnj9Tz8iOJS/EU9o+W61l1h4LL/Y6L1vMbG1J1h8Ifubrj7l4HcoeYJ7KtLVXKPK4+59UdhmFcJaJ/TES/TESciP63RLRCRP+CiN4kom0i+iuc86E1Ulru0JgItNyhccY4j3LH7xPRu5zzf4WI/jQRPSai3yWiDznnv0hEH6b/nir2Ow7asMVCnzx2gxhRSq3vIcqVbcWvaRgzLM41LR8RuupzOedYMOk5Ieqd99oOIkXV+2w/Qq32Yc9FZLal8MePYkQFddNDq67qc2PG0dbbsQNEHrstB9GN6n2mFyJqkrncUth64WgutxVctiwfEbqol5aPwTnH6z1XzaXKH5nLSWBrDC7ZkHMrc3nQdZHBqOaaF8ZYLKxLXKrmQTSEy6Pn9iiXbYnLSHGdiGM4QYQs87DnIspV8R5EDDX7DdPHk7xVnDCWXSddJ8ACoMyl6hiWHym5zJuXMpciY1B9zyhmOLdtO0C2I3M5DTz1m7RhGFeI6H9BRH9IRMQ5DzjnXSL6LSL6o9Tsj4jo35q2L7afbU0oCJfHQczISS8A248oZCzXNmacbD/b8tBPJ4bpRZhQsq24WPwoJi+92ZpedMwfzjPbIGLkBQy+R3G+71HMcWP2gmzbyb4XYkLJ/pjpTmFeFOPm3/fCY/4wyTaIGC5IJxjuTxAz+OMEMQXxeFy6YQzf87gU/vhRTG7qj+VHFCnOl+AyjNnA9qpPCrU/LDu3fkgxP35uZS5daa6p5mXfzXwXNxOZy75qHjCOG6EXMfJDiUs+aMs4DXApzq0dRMd8H/An4rhOnCDGj7VyXrJsHnjSuVXOS87J9MPUlmXXVA6X8nUiuHRy5kFP4tKWuAyjIdcU47D1js7LKQoST13uMAzjV4joR0S0REkUfZuI/hYRHXDOr6Y2BhF1xL+PvP+HRPRDIqLvfe9739/Z2Xkqfms8x9Byh8YZ47zJHSUi+rNE9Aec8z9DRDYdkTZ48suh/PXgnP+Ic/4DzvkPXnvttSdy5KutNqIMsdgjj5uWTw/ShboH+12kULKtaFs1vRC1oqs1EynmJ6sNREXifUHE0EK+07KxUHdjo4noRdhyztGyXet7qAO+s9tB+id8kMc9J8QTk5cqfaR011bqiFjEMbwwRt3tRsNCyvv5WhPRgrBljGOR8aDronb16+02JB7ZH/G+luWjpvrhfg+7w6l4t/wIizl5XIpjhDHDIuNuy8FC3RcbLURTA/6kvtf73sCuaE8KcQwvjNH2vNmwkDZfX28iQ1FxWem6aGm/td1GVKiaazKXiwdqLoWt7UdYQF6rmUjXP11tQMIQ7wtjhoWxvbaDNuwvN1uI3FXnS+by3l4XkpNqHvTcELX+jw/7kOTy5qWoYd5q2pAdZC7FMWQuD3uDXIpIWOVP2w6w1cLiQQ8SmIpLJ4jQN7FeV3M5DZxFJP06EX3JOX8z/fe/RslN+heI6Nc554eGYbxBRB9zzv/UsM960oVDy4/owkyRDMOgvhfS5bkyERHGMePkRzEtzJTICSKaLRWpWFDbcs7JDmK6OFsiL4yxy5rKVh77UUycE82Vi2R6IV0aYhvFjMKY0/xMkWw/ovlykQo5/jDGyQ1jujBbIjeIqVw0qDTEH3FsL4zJMIhmS8WRvocxo5hxmisXJ86l5Ufwp5DucDbKnyBixDg/MZeTiKRVXIobyVlyefTcTpvLUfPypNeJistR/pyUSy+9TpwgopliYezrRMXlaXHu2sINw/iMiP4m53zFMIy/R0QX0j+1OOe/ZxjG7xLRy5zzvzPsc3R1h8ZEoOUOjTPGeZM7iIj+d0T0Tw3DeEBEv0JE/1ci+j0i+vOGYawR0Z9L/z1VfLRcG9rKXJNamcdpCxdp0f29rJU5ry387VO2hYv62HHawkXqenunjdRsnLZw0cr89hht4fektvChrcz9rJX5pG3hm1Irs6otPGtlNpF257WFi/GB1Mo8CeS1hQs5KK8t/K3TtoWvj98WLlqZR7WFhzGjnzxI/JHbwt9fqmGxL68tXMhT19ebkF/y2sKFLHHStnAhYby7eKhsC39Lagu/c8q2cFF5ktcW/r7UFi6kNd0WPgQ6ktaYCHQkrXHGOI+RtIaGhobGGHihb9Ja7tByx6Sg5Q4td0wLWu7Q0NByh8YZQ8sdOWhaPjrYRJQsj4OI4Ve46wSIKlW2MeOoo+57IX7pVbZEhHpMJ4hQq90wfUQTqvd5YYwIq20H+PVW2UYxQ6Tdc4f7wzlH9GP5ESJQuW06zx+RibQsH1Huk3LJJC5NL0R2MUku/ShGy/YkkMeliEAnyWUYM9Qid50AEfqkuRR17w1z+HUic9mxA3Qc5s1L8Xitceal8Md+Clz2nHAkl+LcDnA5we0FVHihb9IHHRdtuxuNrFdfjG0/omp6gqr9bP8L2XY9TR+9MEaq1LKyvv7tVraHhHhfGDOkeR0npLaV7pHQcdD6Kmw557SJ/R0iakh7dzjpBBc+yGNH8qdhemj33Wxm+wyIY/gRo720YaRtBdSR9psQF5ywZYxDyum5ITXNbI8ET+GPeJ8TZFzW+tmeDSrevSimg3R3tGYOl+IYMpddict9iUvZH5nLSV5c4hhBzLADYscOqONk+18EUT6XfTfEDaDS9dDePmpe1vo+WuhV89KPGLhsWQF13cQf1byMYoYdB7tOtnfHQddF67nKH8uLqIZ56ZHj588DN4zpMJVnGma2l8iWYl4GMaO9duJ72w6kvUSyfWvEMQa49DIuD3vZfhzKeeln/tRMjywv/xr3I0YH3cwfweVOy9FyRx603KExEWi5Q+OMoeWOHNzf6+JXVixqyeOOHWCx4vFhH2mRytb2I7TqbjYsLObc3GwhYhG2YcywAHjQdREJ3tntIBoVtpxzLF42TB+Ptlo86CEKUfnT90Is/KzXTUQWX2y0ELEIWy+MsW/2bstBG/at7TYiaWHLGEebca3vYVHvwX4XmUYel+Lp08vVPqIila0TZFxuNW1w+dVWW8mlWACsdF20tKu4FN+fKJG6BJeTgDiGH2Vc7rUHuRSRtMzllxKXGxKX1hAuu07G5UrVHMqlG8RY3N1u2mjD/mqrjehP2EZHuBQt7XdHcNmyfCw2L1X6kD5U/pheiCd5r9ctSAlfbh6flwmXbXApFr9v77QRSau4rEtcPtzvQbZR+dNzQlpK90RfrZmQYsR3O8qlWNzdbtrIVL/ebk81ki5N7ZOfAXz7pXmaKxWJiOgXXruI18X4wmyJXjfmiIjojStztDBTyrWdKxfp2y/NExHRq5dmaSZ9kvfPvXqBigVjwLZcLND3XlkgIqKXFsrYQeu7Ly3QbPrUYWFrGAb9ydeShsxLcyU8lfhbV+dpoZzv+0K5SN+6mvjz2qU5fO6ffO0CJftXZbazpQJ97+XEn5cvzlDqLn3vlQU8kVzYFgoG/dyriT9X5stJWzURffvqPM0N8efCbIneuJJw+frlEVyWJC4vzlCpkPjw5qsLSi7/RMrl1RFciu8vuCwXJhejiGPMFDMuX7owQymV9L1XFnDuZC5/PofL+RFcvn454fKbl2fxPpXtbKlA30m5fEXm8pWF5Enpkm3pCJfiB/E7Ly1gPqu4vDhXwue+cWWOFmbz/ZkvF+lbVxPfX7s0i3P0868en5czxQJ9V8zLCzP4rO++vECzR65bmcvL82WaSzn51tXhc21htoh5+c1LczQ3k10nai4XjnH5JyQupwEtd2hoaLlD44yh5Y4c6DppXSc9Keg6aV0nPS3oSFpDQ0fSGmcMHUlraGhoPKN4oW/SHy3XsPKbJ3eIFeNx5A6xUfj9vS5WxvPkjndOKXeI1e5x5A6xGf7tnTaqDMaRO0TVwztjyB33JbljmHRUl6Sjk8odQjrKkzuEdLRez7jMkztESnzQdSEdTQJ5csdqbbjc8ePTyh0b48sdgstRckc0IB1lcscHS7Wh0lFFko6urzfRPJMnd3ySynAnlTuEdPTuYlUpd/xYkjvunlLuENUveXLHB5LcIbjUcscQaLlDYyLQcofGGUPLHTkwpYdfiihQHseMSw/8zB4OqrJNHioqHpo5+IDNo7byWH7g5yjbSHp4quVnD2VV2TLpAaRuEOOXftQxkofojudPGGcPoh2Hy+xBtOeLy0lgklxafnQiLoed29NyKT9k2ByDS3GdyA/RHWdehmPOSz86GZfjXicn4VLmIo/LaeCFvkk/PjTJTk+mnPre3k5SpY4TYAV3vW6hxVf8XX6f5Uf0+DBJx3ZaDlqO7+x0MGmFbRAxerCXRF/VnodW08WDHi4McQzOOcYtO6DNZuLPas3E5JB9F2PTi5AebjYtaqbt0rd3OrgBCFsvjJHaHnRdpM8P9nqYiMI2ZpzupM0addNHG/Fy1cTFp+Kye4RLIdWouLSDGA0Gu+2My7u73WNchjGD5FLr+bSftkA/OujjQh3wJ/W9bQdIVyeBAS7TZo1K16XDbsaluMkIWyZx2TB92k4bcZYP+2QquBRjmcuNuo02fhWXjsTlXtuhWj/jUtyQxPvCmNG93S4RJVKfkMgeVfq4CavObdsOaDNto16tmXiKuHJe+hGtpFUa2y0b0kjevHwILj2qpFw+3B/OZdPyaac9nEvhe88NaS3lcrNhU3vINe4EET1KudzvZFzek7icBrTcoaGh5Q6NM4aWO3KwUjURuYp6X3ncc0PU6G42LCzmqGy9MEbkutd2ECE82O8i3RK2UcwQudb7Hmozlyp9RAjClnOOSLFjB2h7Xq9nkavKH9uP8LTn3ZaDlvb7e11ELMI2iBiircOeiwhh8aCHCEHYMsbxBPWm5aP+eqVqInJV+dP3Mi63mvZILkVN7H7HQd3tw/3ecC7N4VyK70+URKOCy0lA5lIsXlZ73gCX4RAuWxKXq7XRXG7IXDrjcXnQdQe4jI9wGTOOyLVuZhne48P+0Ouk6wRYKF+vW5AEVLZOEGFheq/tIKN6sH98XobxIJciw3tUOc4l5xmXbTsY4FJkASp/TC9EVrItcXk/h0vRjn/QdZHhLR5kXE4DL3Rb+MW5EtqMr86X8boYzxQLdGE2oejCbAktrCrbYsGgi3OJ7cJMES3AV+bLVDhyjGLBwNOFZ8tFKqcn+JLUXvvSQvJ3wzDoivCnVECL64XZEpWL+b6XigZ8nz/ij2i/lf25lPo+VypSIf375bnyMX4Khcyf2VIBbc8X50pUGuLPAJczRbQZ53IpfC9nvl+eLw3nslSkcuE4lwPHWMi4FO3UkwB4l/yZKxfIIIlLI5/LmVKBxGV+YXb0vLwoczlkXpaOcCnO0eX57BhirhUMks5tkUoSl+Uh52umVEAr+MXZ4balQmH8eWmMz+XR64TxzB/VPBDfuSxxuTBTpHIp/dwFNZfiOhngcq6MrRSmAS13aGhouUPjjHEqucMwjLcNw3hzal6dA3y8UkdqJtph5XG976Hd9autNuqkVbZ9L0T958P9HlLpdx4eIhUStkHEUJe8XreQQn34uIY0V9hyzlG7etB10e56Y72JVFHlT8cO0Dp8d7eD1PWnDw6RVgpbL4xRS7tc7UMm+dmjKhYOhW3MOGq8d1o20uNPVxtYyFRyaXrYPe/r7TZkAJWt6YVoHV486CGVfnfxOJdhzFCXvNHIuPxoOavtlY8huKx0XSwiTgIyl6KWdqVqIrV/71EV8ouwZYyjxnu35SBd/3S1ATlIxU/D9MHlrRFcWn5E1yQutyQuhZQ1yGXiz0bDggR2bbmu5FKMD3su6ve/2GhB6lPZdp2APl9L5uW9vS5kibcfquelaMNerZmoOX9/qQb5RcXlXtuBXPHZWgMShsqfpuWjfv/2TlYnLeaJbGv7EXohHlV6kO/eXayezcKhYRh/mYj+MyL6IyL6v3POp1tncgo8aSQdM46UL2/MGKdCwcD/x3kfY5wMI0nBRtkK/se15TxJk8fx/bz5c564lP2ZRCT9PHJ53vx5Frg8LYZF0rmaNOf8vzMM4x0i+j8Q0S3DMP5bImLS3//BE3l1DiATmzcWJ60whm3xFLZChxvXVpiP4/t58+c8cXn0s58UzyOX582fZ8H3aWBUdUdARDYRzRLRpSP/PfPQu+DpXfAmBb0Lnt4Fb1oYJnf8BhH9AyJ6i4j+z5xzZ2penBJ64VBjItALhxpnjNPWSf+nRPSXOee/ex5v0JOAiGzyxpxz1GOGMcMvfd77RNQZxQz1vKOOETOOX+FRtoxl/ohjjeNPeEJ/4jFtmeT7KH9OyqUYPw0uJ4Fnhctx/TkJl7I/QTS962RaXMrXyZNyOQ3k3qQ55/8a5/zRVI9+xvh6q4Pqjo8e1/G6GDdMHyvuD/a71EhXrVW2fS9EyrdSM9Ge/PFKAydT2AYRwwr3dsvGk4lvbLQgdwhbzjlWlKt9D22pd3Y7aFBR+dOxA6R8S5U+ni59bbmOiShsvTCmG6mss9Gw0J78+VoTE1jYxozTxyuJjHLQdWk5Tee/3m5DOlL507QCrLg/2O8iJVbZmke4FE8y/0TBZRgz+mw14XJH4vKLjRbkDvkYgsuamXE5CQxwuZ5wudmwIHt9vtbExSxsWQ6Xt7bbkDvyuBQy08ODHtWHcGn5EbhcrVmQvT5ZaeBGJnP5acrlbttBu/SXm+3hXPZ9SCP39rqQ4VT+9JyQbqWVII8PTaqk1RTXlhvKeSmkiK2mRVvplgjX15uQO2Qury0nXFZ6LrZouLXdRnWHyp+WPchlre8PfDfZ1vYj+nIz8X2tnnH56WpTt4XnQcsdGhOBljs0zhi6LTwHOy0bkaKoDZbHth9hIeGg6yKaUNkGEcMiSN30EAmt1y1ECMKWMY4FnI4doK50q2njF1l1DNMLsUi013YQTahsvTDGL3215yFjUNlGMUPE17R8ROgbDQvpqLDlnGPBpOeGaI3dbTmIFFXHcIIItdqVrouFqDwuRZ153fQQCU2SS8uPwOUkoOKyZfmIKjcbFrKAQX8kLvuT5zKMMy4bpo9FtFFcdp0A2c5204ackcelqC/e7zjIBkfNy1rfQ/also0Zx6LxSbjsexmXo64TN4ixkdRhz8VWC3lcipp9mcuNRsblNPBCt4WHMScGDUrWrpIx45yiOPl7HHM8iTrPNmTJOGYcNzdZ9xS2nCj7XJ7ZRjFDa7B8jCDi6TGIIvkYQ3znnCgSn8sYMVYc+Kzj/qTfg3HiaUVRFHOlP6FkKy6WkDHiQ/lJOBzLd+IUpraMEcWF7HtwTmQYg74Lf2Ke+RPFTHm+xPePGQeXk0CeP0bqQxjz9EI2pHOUabmc84HzNYpLcb5Gccl4xmXMONqXVVyS7Lv0uXn+ZPNSuk5G+CMfIxq4ThJ+DGOQH8FJzDkR/BnOJWPZ+1TX31F+sjmT+a68TqTrL3lf9n0El9OAljs0NLTcoXHG0HJHDm5sNCEDvJfWCRMRaiEbpo/a1bu7HaR/4u/y+0wvRE3148M+UroPH9fwSy1sg4ihVnSraaN1+LO1BlJFcQzOOcaHPRdt2Le225AlZN/FuOsEqANePOghHX1/qYbUTNh6YYxHba3XTaTrH6/UIQcJ25hx1DDvtR20YX+x0RrKZdPysZB5b68LmUTFpeVHqKlermZcfrR8nMswZmh73pa4/HytCXlK9kfUDFd7HricBNRcWkjXP1ltQMIQtkzicr/joA37y80WZADVuW1aPlra74/g0vYj1FSvVE1Ich8t1xCNi/eFMcOC2U7LRr389XU1l+J9tb6HBfbbO23IEirfe26IlvbFgx5kmw9y5qWo9d9oWJBiPl1tQMJQcXnQddF7cHOzBelR5XvL8tHSfn+vC5kkj0uxkLlaMyEjXVuu64XDPDxpJO0GMXZCc4IIO8yJMWOcgpjRXLlIXhjTTLFAhYKhtJU/z49iKhoGlYqFXFsxFqnSTGm0bZyWjQl/ZksFMgy1P5xz8qPMtlwsUHGI72IcRIwMI9kdbJRtFDOKOafZUnFqXAYRo4JBU+VyEpH0pLmcK+ef2/PM5Sh/OOfkhQzXSakw3rwUssW0uTzJdaLi8rQYFkm/0DdpDQ0i0nKHxplDyx050G3hui18UtBt4botfFrQkbSGho6kNc4YOpLW0NDQeEbxQt+kP1quoSIhT+74cnN8uUOsjN/f66LoPU/ueOeUcodYiR5H7hBVBrd32ijYH0fuEBUS74whd9yX5I5h0lFdko5OKncI6ShP7hDS0Xo94zJP7hAp8UHXHXh69JMiT+5YrQ2XO358WrljY3y5Q3A5Su6IBqSjTO74YKk2VDqqSNLR9fUmGory5A7xcIyTyh1COnp3saqUO34syR13Tyl3iCqoPLnjA0nuEFxquWMItNyhMRFouUPjjKHljhzU+h4iM1GvKY+9MEZU0LR8REIq2yhmeIxR1wmw0KKy5ZxjgcL0QkRNhz0XHViq97lBjOi5bnqIclW2YcxQP9u2A0ToKlvGOKKxnhsiu6h0XUQ3qvc5QYQopd73EE2obP0o47Jl+YiEVLYx4+Cy54TgsqKwlV+3/AhcVnveUC69MONyEpC5FNFY38u4POy9GFw2TH/sedmxA0ToedeJzGX/lFyGI7gUC53jcClfJ5aCy2nghb5JyxPqUCL6UJp84mR37IC84LitOEFBzHDh9NyQ7HTyyRNcvC9iHDuXWX6EC7lh+mgtP5QmarV3fPK17QA/GhWFP/KF03Wyi6EqTXBxjJBlF47pZZOvbvporz2UbkJiosoXcsPyKUgvhoqKy4Ch+abjBLgYVLwHEcOF03OzG0tV+lEVx5B/HC0vor6bcanyJ+Mypo4zuZt0ReJS+G56EZle4nutP5xL24+pm+5R0rQCtCKr5poXMpzbjhMquaxIN0XhT186tzKXhyO4bErnVnW+ZC47TkCeYl7K57ZlpfPSDclJgwflvIw51fsZl1bKZb3vo9W9MgaX4hpXzsuQSb6HCGbyuBTXeF+alzXpR3Ua0HKHhoaWOzTOGFruyMHtnQ5+DUVNMRFhwa1l+ViIWjzoIXoRf5ffZ/kRajPX6yZ+fa+vNxGxCNsgYliQ3Gs7WBj7aquNqEgcg3OOcb3voVb0wX4Xu8PJvotxzw2xqLdSNbHo+dlatm+vsPXCGHWu200bNdVfbrYQhQjbmHEstBz2XOwQdme3gyhNxWXbDrAQ9ajSo1Yakai4tP0Ibc/rdQtc3lBwGcYMC5Iyl19vtxEVqfypmxmXk4CKy52WjYWxLzdbyHyELZO4rPY8LNje3c32OVed247E5VKlj+hOxaUTRFhs3mhYSN1vrGd7IIv3RTHDguR+x0F9+q0RXDZMH9sDPNzvIdtT+d73QtTWr9ZMRO6frzWPzUs/itFCLnN584Rc9hVcCt87doDtAZYqfWQdeVyKxebNhoXF+Bsbej/pXDxpJN11Aro8V6ZCwaC2HdDLF2aIiDAOY0ZuGNPluTL1vZDmy0UqFwtKW8Y49b2Qri7MkO1HVCoaNFsqKm3lsRfGxDinhZkSdeyAXhpiG0SM/CimS3Nl6rkhXZwtUTHH95hxsvyIrsyXyfIjmikWaKak9p2IcGwniKhgGDRXHu27H8UUxZwuzJZGchnFjJxTclksjOfPUS6vLpTJMNT+yFxOIpJWcekGMRkGnZjLnhPSpbnSWFyaXkhzQ7jknFPPfXpc9tyQLswUqZTjT8w4WV5EVxaSeVke8zoRPxLzM+NxGcacLqZcXpzLv06imJEdxHRlfjwuu0449Do5LXRbuIbGMGi5Q+OMoeWOHOg6aV0nPSnoOmldJz0t6EhaQ0NH0hpnjHMZSRuGUTQM465hGD9J//1zhmHcNAxj3TCMf2EYxpOJPBoaGhrPAc5S7vhbRPRY+vffJ6J/yDn/BSLqENHvTNsBLXdouWNS0HKHljumhTOROwzD+A4R/RER/WdE9B8R0f+aiBpE9DrnPDIM49eI6O9xzv/CsM/RcofGRKDlDo0zxnmUO/4LIvo7RCR+fl4hoi7nPEr/vU9E31a90TCMHxqGccswjFuNRkNlMja6ToBuQNENJ4/DmCHS7nshfi1lWxHNMsZRt2z7EaKmtuJz5bEXxoieVX+XPyOIGGqRe26IqLKtsI0ZRzRm+REi4lH+uEGMKGWUP34Uo86854TgUnWMKGaItE0vRKuu6hhJqVMydoJI6Y/qGDKXXSdAZKaylbmcBFTHGIfLzgguVd85j0vVPMjjMm8etCUuRfQsc6myzbtOVMeQrxNLuk5G8ZPHpeoYk56Xo7iUbaeBp36TNgzj3ySiOuf89mnezzn/Eef8B5zzH7z22mtP5MtGwyY3JfrhQRYNiXHfDWknTcd2Ww7107ZU2VakhE4Y03qa/hz2XLS+Pj7s42Yq3hfGjJbT1K1h+lRNZZS1uoUTL2w550jhu04A2WK7aaNNdlHhj+VHkFz2Ow4m16NKDxecOIYXxrSWbmBe7Xso6F+umri5C9uYcTQutO0A6eFG0yIn9X1RxaUXIbXdbTtoOVbx7gQxUslK18NFInO5KHH5OG1KOc4lO86P4NIN0LQzCSxKXAqJo9b30Na8UjvOJWOcHlUyLkXTzkbTwrYCqrlmSlzutV38GKvmgRtmXB72PGqlXC4f9nEzFceIYoYGn6blQ0ZZl7hU+dN1QtrvJL7vNB38+KnmgRVEtNkU59aljp34/qjSPzYv/SimlZTLuumh8WWlZuLmvqjgsmOHaNrZbFpkBfn+mF5EO82MS9FOLubJUS7FRv+HPQ+yzuNq//mSOwzD+L8R0V8nooiI5ojoMhH9/4joL5CWOzTOAlru0DhjnCu5g3P+dznn3+Gcv0lEf5WIPuKc/9tEdI2I/lJq9ttE9MfT9uVRpYf0WF5EEuOeE6Lteb1uIk1T2TpBhIh3t+Vgw6I7ux2kW8I2jBlaY6s9D9Hxw/0eIgRhyznHYmHL8tGqu1I1kWKq/LH8CFHRVtNGG/btnTYiFmHrRzFaY/c7DqLje3tdpH/CljGO9ve66eGJyUuVPtLjPC7FguR63URkr7J1gxjRy27LwYLt3d0OImlhG+VwuXjQQ1YiH0Nw2bYDcDkJyFyKJ2cfdF1weX8Elw3TH59LV+bSApfiu8m2XphxudcezaVYcKv1PWQao7js2AGi9dWaCflA5bvtR8jEtps2otHbO51j8zKIGLisdF1kGg/2u8hKZC7FVgJNy0cW+fiwD+lD5U/fC5H5bDQsSBfjcFmTuJxmJP1kj7idLP4TIvrnhmH8X4joLhH94bQP+OrFWSoXDSIieuPqPF4X49lyga4uJJWAVxdmaLZcyLWdKRbo1YuzRER0eb5E5WJi+83Lc1QoDB6jVDDoG5cS2wuzRWI8ecr2q5dmqFwYPIZhGPT6lWS8MFMiw0g+66ULZZotFYf6I1pVr8yXab6c2L5+ZR6fIWzLhQK9eimxvTRXptRd+salWSod8b1QMOibl+cS32dKNJN+z1cuzmCs8mdupoCW96sLM8lTuvN8LxXotUvHufzG5TkqHuWyWACXF+dKuPHk+ZNxWSSiyVV5ylwK3y/NlSilkl4bxeVsEX9/dRSX0rx8aaEMLsV3G/BHnpdzZSqm8z2XS/hTorkST/2ZHcrl/EyRrvJy6s8MzZaGXCelAr0izUtxTb1+Ze74vCwa8P3iXHarUl23hYJBr19JfF+YKVIx/axXLszQzBB/ZksFeklc4/NlPPH+pFyWitOLd3Uzi4aGljs0zhjnSu44T5hWnfSD/axOWlXbe7ROeild8Hgvp05a1PbKddKfrzVPVSedV4/63pPWSa+crE66NoRLU3ryulwn/dMHhyPqpC1ITu/n1PY+jTppUXMu10m/uzi6TlrINh+foE76q632ieqkNxW1vZOsk75xwjppIan8OLdOOuHytHXSn6w2RtZJ31DUSYt5Itvm1Um//fA5rJOeFHQkrTER6Eha44yhI2kNDQ2NZxQv9E36o+Xa0BS9JqXo48gdIkW/v5el6Hlt4W+fsi1cpOjjtIWLzcpv77SRVo7TFi5S9LfHkDvuSW3hQ1P0fpain7QtfFNqZVbJHVmKbiJFz2sLF+MDKUWfBPLawkWKntcW/tZp28LXx28LFyn6qLbwMGb0kweJP7Lc8f5SDRUSeXKHeNDB9fUm6uzz5I6PVxJZ8KRt4aJa6d3FQ6Xc8ZYkd9w5ZVu4qCDJawt/X5I7RM30c9kWPilouUNjItByh8YZQ8sdORBRKxEh6pLHjHH8YnthjHpnla38eUHE8MuaZyvGYcxQPzvKNmYc0ZgXxog8VLacZ777UYwIdJTvJ/Enihki7fPA5Un8kbmcBJ703EYxgz9uMPzcnkcuZX8mOS+nfZ1Mmstp4IW+Sd/dy54l9/laE6+LcdPOnt22dNhHS63K1pSe3bbRsOgwTUG/2GhhIgrbIGJ0M00P9zsuKkFu73QwCYQt55yuryeSS930aLWapFgPD3poYVX503NDtL6u1Sw011xfb2HSClsvjOnWTvZcPtHie3OrjQtV2DLGIQEd9jykfPf2upCOVP60nYCWUi4fH/apafu5tpYf0d29JF3dbGZcfrl5nMswHuRSNITc3ung4pGPIbhsmD6kiElggMvtxPedlgOZ6autNm4cMpc3Un+q/YzL+/tdMv3jvstcihbo5ao5lEvbjyCjbDYtqnQzLsVNZoDLzYTLg65L2ymXd3bVXOI6sTIuH1WyZ4GqbPtuhIqgtZqFNv4bOfPya4nL3ZTLr7c7uLGO5HKvi+0cVP50nABy40rVpEZamSLmyVEuhYyy3bLRen5zs63ljjxouUNjItByh8YZQ8sdOdhoZBsaiVpleWx6ISKhvXa2cYzK1pM2sqn2PLSXLlezjWOEbcw4Fuealo8FybWaiZROPoaI5ntutnHMdtNGdKPyxw1iROgH3WwTHvFZsm0YM9RG1/vZxjGrNRORq7DlnGMBpyNtsLQ5gkvLlzcFcpDBqGz9aJDLtsQlY8e5FFFcS+JyvZ5taJTHpagdnwSUXJrZZlWrNRPRlsyl8KfrjM+lfUIuRVRZ6w/nkh3hstbPNlhScSnGfS/jcqdlY5Ex7zoRi+qVrotFvceHx6+TKGa4ThqmfyIuxQLgVtMeyaXIvvbaDrJBlW0QsQEuxVYLK1UTXE4D56kt/KmjVDCokLaPijZTeVwwDLR0FwoGWnxVtoZBaOstGITPFa8N2BKhJbdgGPipLOYcQ/5c0e5aHOG7YWTHKBoGWr1H+iN97mh/jAF/0mEOl4Q22sIo3yn73EIh+86lQuHYMY5yyQzB5XHbY1xKXDwpVP4UDQOtzgk/w86XIc0Zte/yuS1Ic2YUl+I7GwZJ80B9DJnLgpG9NvzcGtl3HuGP4AW2hcz2KD+GYQycL9lHla08ls+ByofT+D54jQ++b5rQcoeGhpY7NM4YWu7IwedrTaSKoh5THtdND23Yt3faWHyTbUV7d98LUW/5qNJDOvreoyokA/G+IGKoA95oWEjpPl6pY+FQ2HLOUXdb6bpYdLm52YKkInyQxx07QEv7/b0u0r93F6tIK8UxvDCma2nt6mrNhNTw4eMa0lxhyxhHTfVe20Et7fX1JlJF2R/xvobpo8b79k4HsoSKd9MLsVizVOmDy/eXauBSHCOMGeqAt5o20vVPVhuQgwb9SXw/7LlY6J0ExDFkLtdqJtLjj5ZrWDgcxeWN9SbkKRU/Mpd3dtVcCn8sP8L2AI8P+5DA3l+qQTIQ7wtjhjrgraYNWetTiUuVP9Weh8XJr7bakAFU86DnhKiXf7jfg0zys0c58zLdamG9bmJHymvLdUgY4hgyl/sdicuNJnavVPnTtHzUy9/Z7aDmXMwT+X22H6H3YLmq5nIaeKEjaT+KsZOcasw5pzDmNFMqUBAxpGSj3hfFDFLJKNuYceKcU6lYGGnLGKeYcyoXR/sj+x7GLJE8xvAnihnSxXH8YWP6/iRcjuvPabmcRCQ9CS6FPyfhMowZlQrnh8uTnNuTzEvx4zxtLp/0OjkthkXSL/RNWkODiLTcoXHm0HJHDnRbuG4LnxR0W7huC58WdCStoaEjaY0zho6kcxBLtY15Y1H/yMawFWPOOaKCSdqe1J+n6ft58+ckXE4Ck/D9vJ7bac7LafhzllxOAy/0TfqztQaqO96RV8ZFdUffo1vpc9NuSRUJsu3bUnXH52natHjQRwurXN3xjlTd8QGqO2w8Ofzaclbd8Y5U3SHGB12X7qXPfPtyswW54+2Hx/2Rqzvu7XfRBPPO4iEm1zuKVfQVqbrjA6m64x1FRcJu26HFgyQF/Uyq7pD9eUeqlBHywu3dDholVLybXoiKhEeVPp7YLnP59sPjFQmbzYzLT1brkDveVlR3VLou3Z1gdcfbD49zuVqzkBJ/+Dir7lBxudd28YTqz6XqDtVca5g+fSVVJKi4fFuq7vhU4nJb4lKk6OJ9Uczo/aXEn82mjTZ+ubpDdb4Oey7a+G9utdEMpZoHSXVHMi8fHPSwBYFcdSTPy49SLtfqFp5o/5FU3fG2srrDxZYI16XqDpU/TcvHtgJ3djtoKFJxKVd3LB32IWm+v1TVckcetNyhMRFouUPjjKHljhwcdF20YYvWUHnshTGi53rfw6+3yjaMGaLVluUjQhcLI7It5xwLeT03xMLGXttBpKg6hu1HWJSp9jxEZipbP4qxoNQwfSz8qGxjlvnTdQJEcXttB9GN/D7xnUwvRE1s5YRcioxBZRtJXLbt4ERcitrx/c5wLp0g43ISEJ/LjnLpZFwyhT/iO1l+dCIuRfRcN0/GZX8El+L1vncyLkUPQW3EdRJEDNFq0/Kx1YLKVuay54Qn4rIpcSmywUlwKeq6O0e4nGaw+0LfpE0vxOQT0gERUSedDH7EMIksPyI/Pdni7/L7opjjZuIEMWy7boAJJWxjxnEj9MKYnHRi9L2QIjZ4DM45xkHEkHZafkhhfNx3tT8RJmrHCTGhZH/6ku/iIuu5x/lhjFPXDcCP8N30IoqG+BPEDDu7WX5EQTyESzbouxcO51LsBuiHMbmp7303ApeqcxtEDD9ck4Dsu+DSDWPyIolLfpzLTvoD7UvzYBwuxby0/Xjg3Cr9cWUuk2N03QDnVryPcRqcl2Hmj/jRyOPS8YfbZv4wMtNd6Rw/Jl/4o5qXPLtOXOncqrhMrpOMS3Gztfzh8yCMM39sP0bgkz8vU9/DwetkmrK0ljs0NLTcoXHG0HJHDr7aaiMiEYs98rhp+fQgXah7sN9FCqWytfwIC2OrNRMp5ierDUQswjaIGNqed1o2Fuq+2Gjh11nYcs7RZlzre6ipvrPbgUyi8qfnhKgVXar0kdJdW6kjYhG2XhijhnmjYSG9+3ytiShN2MaM42nPB10XdcBfb7cR/ar8aUlcPtzvQWrI41LU3a7VTKSYnyq4DOOMy92Wg4W6LzZaiKYGjpFyWZe4nARUXG42LLQOX19vIkoTtoxx1AxXui7qgG9ttxGNq/hp2wG2B1g8GM6l7Ud0M11AXquZkA8+XW1gsUvmUizY7rUdtGF/udlCBqc6Rt30UFN9b68LmUQ5L90QWy08PuxD+vg4b16mi/FbTRsLdTdGcHnYy7i8vdNGNJ7H5T2JSyHbiHki2zpBhMX49XrG5WdrDb1wmIcnjaRNL6SLsyUyDIN6bkhX5stERBgnT8tgdGG2RLYf0Vy5SMWC2pZzTpYf0aW5MnlhTAXDoJlSQWkrj/0oJs6J5spF6nshXZ7LtxVPp1iYKZHlR7RQLlIhxx/GODlhTBdnS+QEEZWLBSoX8/0Rx/bCmAyDaLZUHOl7EDFinNNcuTiSS/H0DsHlbKlApRx/ngaXUcwoSLmcRCT9pFyGMaMo5jQ/czIunSCimeJwLk0/gj/T5tLyI5ofcp3I89INYioVjbHnJdH414nM5YWZUu51chIuj/qj4vK00G3hGhrDoOUOjTOGljty8NFyDSl6Xlu4SG/GaQsXadH9vS7S3Ly28HdO2RYuUsVx2sJF6np7pw3JYJy2cLFp/TtjtIXfl9rCh7XY16UW+5O2hYs0N68tXNSxrtczLvPawkXr8EHXRYv9JJDXFr5aG94W/uPTtoVvjN8WLrgc1RYeDbTYZ23hHyzVhrbYV6QW++vrTciCeW3hQi47aVu4kNbeXawq28J/LLWF3z1lW7iQX/Lawj+Q2sIFl7otfAh0JK0xEehIWuOMoSNpDQ0NjWcUL/RNWu+Cp5Y79C54J4feBU/vgjctaLlDQ0PLHRpnDC135KBl+ehgE/WR8jiIGH6Fu06AqFJlyxhHW6/phfilV9nKYyeIUKvdMH1EEypbL4wRYXXsAL/eKtsoZoi0e+5wfzjniH4sP0IEOsp3L4yRibQsH1HuJLhsSlyK7OIkXDat4Vz6UcblJKDi0p4Sl2Gccdlzwqlw6QbxAJfDrhM/itGy3bEDdByqbGPGMS/7I66To1za0nUyLpdtOxjJpajr7jkhsp1RXFp+pORyGnihb9J7HRetpus1C6+LNMbyIzpMU8nDnodJIv4uv88NY+zo1TB9tCpvNmxMEmEbxgw7u7XtADf33baDdnJxDM45xqYXQXI56LpkBwrf07ETxkjd6n0P7awbdRs3L2HrRwy79rWtABfRTsvBBSdsGeO02UiknJ4b4oLZ77i44FRc2hKX1b6HG4CKSy86wmXahr41gsuOE6q5lPzZqNvgUjT4TALiGEHMaLedHCM5t4nvuy0HN9NRXB50c+ZlLeOy0h2PSz9i4LJpBQNcih958b4oZrTdFFwG1Ez92Ws7aONXnVvTi6iW3qgqPRct4sp5GUR00BHz0kfLumpeHuVSzMvdto2bqYrLvhtSvZ9y2XHxQ6ny3fFjqqQVHdW+R5Y3nEshGzZNH23o201Hyx150HKHxkSg5Q6NM4aWO3LwYL+LX1mxQCiPO3aAhZ/lah9pkcrW9iO0PW81bURpX221Ef0J2zBmqHc+6LpYPLm720E0Kmw556jVbpg+WnUfVXpI6VT+9L0QC5LrdRNR2pebLUQswtYLYyy07LUdtLTf3mkjkha2jHEsEtX6Hhb1Hu73kGmo/Ok6ARZ+VqrmUC6dIEL99VbTxsLY19tqLsViamUEl+L7EyUpvKgHnwTEMfxokEtRn357p41IWsVl/QiX1gguH6d7Pa/WTESYKls3iMHldtNGHfDX221Ef8I2OsKl2B7g3l53KJcticulSh/Sh8of0wuxILnRsCAV3FTMSz+K6faOissOImmZS9H+Xjc9LJAuHgznsueEtFTJuBSZmPhuR7kUC+U7rYzLWxKX00Bpap/8DOBbV+fxlN8/+doFvC7GF2ZL9I30tW9emqMLs6Vc27lykb51dZ6IiF65OEPlQvL79+YrC1QsGAO25WKBvvvSAhERXZ0vk8hlvv3SPM2WCgO2hmHQz7+ajC/NlWimmPz9jSvztFDO932hXKQ3riT+vHZxjmbLyft+/tULZBiD/syWCvSdlxLbly7MkJF+1ndfWkiepi3ZFgoGvflK4vvluTLNzyQ+vHF1juaG+TNTom9emku4vDyL9ym5LBXp2y8d5/JPvKzm8nsvp1wulHET/85LC8e4FN+fiOjibAmfOwmIY8wU87mcKQ3hcr5Ms+WMy/kRXL5+OeHyG5eGczlbKmBevnyEy9KRc1vK4fLbV+cx75RczpVwXl6/MkcLs/n+zJeL9MaVxPdXL87iHP2cYl7OFAv03ZcVXL583J9CwaCfS/25PFfGdf3GlTmaU8wDcDlbpNevHOdSfLejXH5bcHlhBt/5exKX04CWOzQ0tNyhccbQckcOdJ20rpOeFHSdtK6TnhZ0JK2hoSNpjTOGjqQ1NDQ0nlG80DdpLXdouWNS0HKHljumBS13aGhouUPjjKHljhxYfoRfb7GvtDyOGUc05gQRojiVrXiaCFESAYj6YpWtPA4ihghrlG0UM0Tath+hVVdlyxhH9OMGMX7pRx3Dj7IHm46yDWOGiOa8cCn8OQmXk0Ael+Oe29Ny6QbxUC7F5xElXI57bmUuxfvzbGUunWD4vOQ8m5cnOben5dIewSU7wuWo62QUl9PAC32TfnTQQ2u1nPqKcccJkNKs1Sy0gapsLT9CUfxOy0Ezy+2dDi4iYRtEDDLBYc+lvXaSYj086GFyCVvOOd3aTlK3phXQZjPxZ6VmQqpR+WN6ES2nqfZm06Jm2p58a7uDSStsvTCmh2lqu99xkfLd2+tiIgrbmHE0GNRNHy3ZS5U+JrDKn64T0FraXrtetyDVqGztIKZHqT+77YzLO7vdY1yGccZlteehBXrxoI8bh3wMwWXbDpD6TwIDXO4nvh90XDpM27fv7/VwkxG2jHG6JXG5nTaPPD7s48nqeVyujsulH4HLvSNcihuSzOXd3S4RCS6Tc7t40MONTHUMmcuVqkldN39e9r0IjThbTRt7YdzaUc/LBymXla6HVvgH+8O5bJg+5MbHh33qe0O4dENIUhsNi9pOdp0ctXWCCBLQfifj8q7E5TSg5Q4NDS13aJwxtNyRg9WaichVtM7K474X4hd5q2kjclXZemGMBbf9joP20sWDHtI/YRvFDIuF9b6H9tLHh31ErqLFnHOOcdcJsNCyXreQNqr8sf0IWcBuy0Eb9oP9LiIWYRtEDNFNtedhgfRRpYcIQdgyxhEptiwf0dZJuRQLY+K7HeVSRDcHXRfRVh6XIrqpmxmXy9U+oi3ZH5lL0fY8CchciozqKJfhES45H+RSLO6u1UxkASouTS/EYur2CbkUi3qLBz1kJeJ9MePgsmH6yKhGcdlzQnC50bCQUal8d4IIWxvstR1kAQ/3e8fmZRhnXNb6HiLXpUp/KJdtOxjgUmQBKt9NL0QWsNOy0dKex6VYvKzkcDkNvNBt4eKpxkRJW66AGJcLBVpI20Tny0W01KpsiwUDtnPlIpXTVtSLs8mTio/aXkxbzGdLRWLp5Lwwk7XXXkqfhmwYBsblYoHmZpLPXZgZ7nupKPkzU0BL8qW5Mtpv1f4UqJD+/eJs6dgxCgWDLs0ltjOlAlraR/lTLhTQ6rwwU0Rbr/huuVyWCiO5FP7MFosUFzIuS4rzJXMp/JkE8rhMqUy4PMJ7cm4zLsV1Pj+Ky2Ihecp5alsuDs4Z2bZ0hEvRvnxxtkTpIfC+gkHwfaZUgA8XZo77Lr+vXDIGzm1piO/FgkHzqe9z5SLm5cW50vF5aQxyKTCKy3LRwBYFC7Oj58HANV4azuUFyXfBj8zlNPDU5Q7DML5LRP8NEX2TiDgR/Yhz/vuGYbxMRP+CiN4kom0i+iuc807e5xBpuUNjQtByh8YZ47zJHRER/cec818iol8lon/PMIxfIqLfJaIPOee/SEQfpv+eKj5ZbWBlVtSHyuN638OiwVdbbaSuKtu+F+IpyIsHPaR/7zw8RCokbIOI0XtpXfJ63UIK9eHjGtJcYcs5Rx3wQddF/eeNjSZSRZU/HTtALe3d3Q52tvvpg0OklcLWC2PUJS9X+0hH33tUhfwibGPG8aTznZaNFPPT1QbkICWXpoda2q+320hdVbamF6KWdvGghyevv7t4nMswZqjx3mhYkG0+Ws6ecC0fQ3BZ6bpYAJ0EZC5FXfJK1cTucO89qkIyELZM4nK35SDF/mytAQlDxU/D9LHj260RXFp+NMDllsSlkLJkLkWN92bDgtRwbbkOaU3F5WEv4/KLjRbkKZU/XSegz9eSeXl/rwtZ4u2H6nkp6pJXaxmX7y/VIK3JXIreg722A4ni87UmJAyVP03Lx453t3eyp4WL7ybb2n5E11Iulyp9SE7vLlaf74VDwzD+mIj+X+l/v845PzQM4w0i+phz/qeGvfdJI+koZkj/8sYx41QsGPj/OO9jjJNhJCnYKFvOOXGeyAjj2DJOY/sj+14Y0x+h+Y7rz7i+n2cuJxFJay5PPi9P4s/T4vIk14nK99NiWCR9pjdpwzDeJKJPieiXiWiXc341fd0goo7495H3/JCIfkhE9L3vfe/7Ozs7T8tdjecRcUhULI+2m/ZnaLzQOG9yBxERGYZxkYj+eyL6DznnfflvPPnlUP56cM5/xDn/Aef8B6+99toT+fDRcg1yR15buEiFxmkLv7acpEL397pI0fPawt85ZVu4eFjAOG3hn61lbeGiCmOctnCRVr4zRlu4SCuvLdeHttjXpRb7k7aFixQ9ry1cpLnr9YzLvLZw0Tp80HWTFvtimT5fa6IaR+VPZ6DFvoMUHa3MxXJuW/hqbXhb+I9P2xa+MX5buOByVFt4NNBin7WFf7BUG9piX5Fa7K+vNyF35LWFC1nwpG3hokrl3cWqsi38x1Jb+N1TtoULuSOvLfwDqS1ccPlctoUbhlEmop8Q0c845/8gfW2FnrLcoaGhoXEecK4i6VTK+EMieixu0CneIqLfTse/TUR/PG1fRJSYN+acox4zjBl+6Ue9L4oZNLRRtjHjiA7H8SeS/Bn1PYRNdALfT+IPY5k/0+IyZnxsLtlT4nIa5/a0XJ703D4NLkf58zS5HHVuJ83lNHAWcse/SkR/nYj+dcMw7qX//UUi+j0i+vOGYawR0Z9L/z1V3NxqQe4QKaE8bpg+Vtzv73WpkaZxKtu+F6J6Yblqoj352kodk0vYBhFD+rzdstF0cn2jCblD2HLOsbveYc+jxXTF/fZOBw0qKn86doDW1keVPp7U/dFyDRNR2HphTNfT9Hm9bqE9+dPVBiagsI0Zxwr3fsdF6/lXW23IHSp/mlYAaeTBfheNACpb0wvp5lYr5bJPe6lU87GCyzBmSJ+3WzatpZUpNzaaSNHlYwguq30PrfC3dzqQjlT+dJ0A6fzSYZ8O+yO4TNPnzYYFqeaztQbkDmHLGKePUonsoJtx+fV2G3JHHpeiFf7+fo/qQ7i0/AiS3UrVxFPhP16p40am4nKn7UCq+WKzpeRSjGt9H1ze3e0O5bLnhPT1VsaleFL3R8t1JZefrzckLpPr5PP1BuSOPC4fH6ZcbrVR3aHyp2UHaIV/cNCjWvqUcTFPZFvbj+iLlMvVmkk7KZefrDaeP7ljUtByh4aGxvOAcyV3nCfsthxEiiKaTcbJr7ATRGiNrXRdRBMq2yBiWASpmx4iofW6hQhBvI8xjhrLjh1g0Wq7aeMXefAYydj0QtTE7nccRBPCB3nshTEWC2t9DxmD6nOjmGGhs2X5iNA3GxZSOmHLOce454Z42vMgl+axYxzlUtTdqvyRuWyYPiKhjYbMpXmMy64TYNFqkMvj/lh+hAW3QS6P++OFMRYL87lMjhEzjuh5FJfyuOeGWJjeazuIulXHcIMYde+HPZnL4/MgjBlq9vO5zM7thoLLnZYNSUDlj8zlQddFNqjiXeay3veQfak4kbls2wEi9K2mjYxKdYy+l8flcdt8Lo9/T5nLpqXmchp4oW/SQRyjJVtcpMk4051kHVVMDJUt45wCaFuD+pk4f+J9nCizZZwiYRsztAbLxxCTjLFM/wpjLvmepVoD/kSZ74wNfta4/vAjtuI7CX6iWPZd5U98jMso5hQreY8lLuPUHwZbP5S5ZPDdjzLfYyWXmT/i+w+eW55zbjN/VPPAj2JcnCreY8YpTIkf5CflnXPp3HIK8bnH54x8jJhzCsW5jWQu1fMAvDNGUerPIJfie0rrKvK5HeWPzGU0fB5wns21UNJ1B7nM+Mn8yXxP/Bk8Rh6XgTT3lfNS4jKKs7k/eJ0cP7eJbebPFLfu0HKHhoaGxllDyx05+GIjWzgU7adEhFrIhuljgebubgeLXR9ItuJ9phdigWa52kdK99FyDZGXsA0iabGraSOd+nwtWzgUx+CcY1zteahdvbXdRv3n+wp/uk6AR20tHvRQ//nBUrbYJWy9MEar7nrdRIr5ibRwKGxjli1k7ncctGF/uTmcy6blo3b13l4XMomKS8uPUFMtc3ltuX6MyzBmaHveadmo8b6+ni0cyv5ki10eWtpv77QhS6i47DkhFg5lLj98rOZS1Kev1y1IMZ+sZguHwpYd4VK0Yd/cbEEGUPnTsnxsD3B/BJe2H6GmeqVqQka6tpwtHH4gcXlN4lIsHN7I4VK8r9b3sMAuL8IquXSzBfZHlR4ksDwuxQL7RiPj8tPVbOFQxeVB1wWXX21li7Aq31uWj5b2B/tdyCS5XKaLwqs1iUtpEXYqSFoon83/vv/97/Mnge2HGFve8XEcM+4GEeecczeIeByzXFv587ww4mEUD7UV4yCKuR/GY/kTSf44fsQZy/eHMcYdP/M9GtN3P4x5MKbvYRRzL4zG8v28cznMn6fN5ahze5TLcf3xwmhsf07L5ahze5TLcc+tH2b+nAcu887taUFEt3jOfU7LHRoaGhpnDC135EC3heu2cCJ68rZwOtrKrNvC82x1W/jJoSNpDQ0NjTOGjqQ1NDQ0nlG80Dfpj5ZrQ1P0mpSijyN3iNXl+3tZip4nd7x9SrlDpOjjyB1Zit5Gij6O3CFS9LfHkDvuSXLH0BS9n6XoJ5U7NqUUXSV3ZCm6iRQ9T+4Q4wMpRf98bXiK3rGzFP2kcodI0fPkjrdOK3esjy93iBR9lNwRxgwb3Mtyx/tLNTR55MkdomLj+noTVVB5coeoxjmp3CEejvHu4qFS7nhLkjvunFLuENUmeXLH+5LcIRpetNwxBFru0NDQeB6g5Y4c1PseIjPxCyqP/SjGglLL8hEJqWxjxhFp95wQUZxYiDj6PhH9WH6EaL7W99CBpXqfF8ao522YPrq8VP6EMUNE07EDRB4qW8Y42s37XoinPef5Ll53ggitsXXTQzQxDpfD/Dkpl+L1PC5VtjKXTctHxjCKy64TINtR2XLOcW5NL8TCdLXnIVLM41JEfCfhsj3i3A5w6YaIiGUuVWPbjxDN53Epz8v2mFxGMUNd97S4dIN4JJfCNogYsiiZS9Vci6XrJI/LaeDFvkmb2Y1X7FpHROjld4Ns8rXtbEIdSCdbvM+PYuxG1nUDsrzkBFa6Lia4sA1jhhNreiFudNWeh5ZZYcs5x/FsP6K2k10MYkLJvouxF8bZ5HMC3HgrXRcTHP4whouh54TUdzN/wiP+MMYxaS0/oo64GPr+Md9lrryAUUviUviu4jKIWA6X2Y+qsI1ihh3+LC/70aj1j3Mpj20/gj9NyydPMQ9kLsVNum0HZAf5XAYxG7iQTS+7kMN40PYol93U94bpo9Vd6c8Al/7QeRnGGZc9J5TmwXAuTS/CPBh1bh3pOmlZAbnD5mXEqGkmtp0BfxTzMuZURfAQUT/lstr3RnLZkbj0hnDphjG1rIxLJ8j3PYwZ1dNd8voD59bTckcetNyhoaHxPEDLHTm4s9tByiLaouVxy/KxqPeo0kO0INuKWmTbj7Dws163ECnf2GgiYhHvC2OGpz3vtR3UVH+93UaEKWw55xjXTQ8LUQ/3e0hHhQ/yuOeGaNVdqZpIMa+vNxGxiM/1whiLaNtNGwtjNzdbSF2Fbcw4Fq0Oey4WT+7udhAVyf6I97XtAFwuVfpI11W8236EhZ+NhoUISeZSHCOMGWrZ9zsOFmxvbbcRYcr+iEWihuljIerhfg8RuMqfvheiHny1ZkI+kLkUx5C53GkN55JJXFZ7HrYHuLfXRWqvmmsdO8Ci3uNDNZfC1gkitD1vNCxEvzc2moj+xPuimGGhfL/jYMH29k7GpYofmcvFgx6kBtU8kLlcq5nIOlTz0o9iLEjuthwsMn611UYGLI4hc1nre6j1l7lU+dN1BrlsjuQy8WdT4vKLjZZuC8/770nbwtuWjxbWpunhdTEOopj33IBzznnPDdAGqrKNY8Y7ts85T9pERaupypZzzltWYusGEVpNW5aPFlbV+/ww5v3Un64doIVVZRvFjHftxLbvBmipVdkyxuCP7Ydo2xWv5b3PDSJupi2xHXuyXLat8bmU/RFctk/IZTjEH5lL0wvRcjzq3Dp+NDaXXjg+l2EU864zHpeMPWUunfPH5bDr5CiXo66TUVyeFqTbwjU0NDTOL7TckQNdJ63rpIl0nbSuk9Z10lODjqQ1NDSeB+hIWkNDQ+MZxQt9k9Zyh5Y7iLTcoeUOLXdMDVru0NDQeB6g5Y4c9JwQv97i11YeRzFDjaXphfi1VNlyzhH9OEGEqEllK4+9MEb0PMo2iBgimr4XIqpU2caMI0uw/QgR8ahjuEGMKGWUrR/FiFZ7bojOyolw6TwZl6PObRgz1HVPi0svnD6Xlh+hK/RZ4JKx7DqZFpfydTItLvOuk2nghb5JrzdMstOJeD993p087rkh7aTp2E7LweRS2dpBjPSn0nXRarp40MekFbZhzOjxYZIGN0wfra+rNQsn/kFqyznHuOsEtJdu3r/VsNEurfLH8iPabCSSy17HwUR6sN/DBSdsvTBGWl7te2h9fXxo4iIStjHjtHiQpJ0tK6CDtGV2vW6RE+Zz2feiAS67KZcPFLZOENN6wwSXzZTLRxU1l0vpcxYbpo8mopWaiac8y/6I43WcALLFVsPGhTqKy/2Oi1b4hwcjuOwN55JJXLbtAO3HGw0Lred5XG43BZc25qWKSzeMaa0uuPQgRTyq9PFDKd4XxQzPBmyYPlVSLlfrw7nsOiFki+2mjXZyJZdBBPlqv+NCslNx6UcxLadc1voeGl+WqyZ+bGQuH6byTNsO0Giy0bDIUnApfDe9CNLkbstBa34el6uCy54LiWxJ4nIa0HKHhoaGxhlDyx05eFTpIaUT7Z7yuOeEiI7X6yZSHZWtG8SIQnZbDtqw7+52kG4J2yhmaI2t9jw82urhfg8RgrDlnKOtt20H+NVfqZqI/lT+WH6EiG6raaN1+PZOBxGLsPWjGE/OPui6WIi6v9dF+idsGeNYlGmYPiKopUof6bqSSzdE2/N63UJkn8elWEzdaw9yGSu4FIuXtX7G5eJBD1nJ4DEyLkVEt1obzaVYtNqWuLyze5zLIGLgstJ1Edk/2B/N5U4rObePD0dzKdqeNxrDufTCI1z2x+dSZBr5XCbjjh1gQXKtZkIaUtnaR7hsjuBSbG1Q6bpY1Huw30VWouKyaQ1yKaQPlT99b5BLsTOimCdHuRSLqTKX9/a6U42kS1P75GcAr1yYpXLRICKib1yaw+tiPFsu0JX5MhERXZmfodlyIde2XDTo5QszRER0aa5EM6XE9rVLs1QoDB6jWDDo1UuzRES0MFskzoqJPxdnqFwYPIZhGPSN1Ha+XMREfmmhTLOlYq4/M8UCvbSQ+H55rkQLM6X077NkGIP+lAsFeuVi4vvFmRIZ6U/3q5dmqXTE90Ih82dhpoi/v3xhhmaK+fzMlgp0ZX4m5bJMc+V8349yWSpmXBZVXKa+L8wUiaVcvnxhhspKfyQu03N7db6M85XPZXKMy/NlmkvnwWsXj3NZKhjg8sJsidI/0ysXT8al2vdkPFcu0JUFMS9HcVkYm8tSsTDA5VxJmpdD/JmfKdIVnvqzUKbZYVyW1Fyq5mXC5aySy6PX7VEuC4Y0L4f4M1sa5HJ+RnA5q+RSnNtLcyXw9+rFGfA6DWi5Q0NDQ+OMoeWOHFxbro/9tPAvN8d/WviD/exp4ara3iBiqP9cq5mQSd7LqZMW9Z/y08I/X2ue4GnhHcgAefWo7ymeFv7uorpOWtTSDjwtfGX8p4Xf3GxhESivTlrUnD/c70Hi+emDwxFPC7eQ2r+f84Rr1dPCr6+P/7TwO7tZnfSPc7gUNefL1azm/N3F0U8LF1LDxyd4WvhXW+2RddKCy8WDHiQeubY3j8vTPC38xgmeFn53DC5FzflK1Rz7aeF77exp4Z+sNkbWSYua86+3s6eFi3ki2+Y9Lfzth7pOOhdPGklzzpFi5Y2f9H1naXve/FFB+/N8+X7e/Hnavp8WOpLOgUxs3vhJ33eWtufNHxW0P8+X7+fNn6ft+zTwQt+kP1qujS13jNMWLuSO+3uZ3JHXFv7OKdvChdwxTlt4Jne0IXeM0xYu5I53xmgLvy+1hY8rd5y0LXxriHQ0mKJnXOa1havkjs/Xxpc7TtoWvlob3hb+49O2hW+M3xYuuBzVFh4NtNifTu64fgK546Rt4ePKHbutTO44aVu4kDvy2sJVcoduCx8CvXCooaHxPEDLHTkQv8ZEhAhWHjPGEf34UYx6Z5Wt/HlBxBDx5dmKcRQz1M+Oso0lf7wwRuShsuWcwx8/isf2J4wZooJx/BGR9nnj8iT+nITLk/gzTS7lc3sSLsf15zxyeZLrRObyJNfJuFzmndtp4IW+Sd/Z6UDu+FR6/pkYN22fHqWVF48qfTyhWWVreiGK6dfr2XP5rq9nz+UTtkGUPZdvr+MOPONQnHBhyzmHbDHwjMODHlpYVf4kzzhM0tXVqoWGkM/WGpi0nyqey7fdtGk3Tee/lJ7L96n0LDmRHla62TMO7+x2IHeo/GnZAVqgH1X61LT9XFvLj+iO/Fy+zvFnHH6qfMahC2nk6+02UnT5GBmX/gCXnRFcys84FJUpn0vP5ZO5/Ep6xuGO4HKrhRuZzOXn0vMiRfv23d3uUC7bTva8yMeHJuQFla3tZ8843Gyqn3Eoc/nFZhNcilb4W9sdJZdi3LB8Wk63OVg8yJ4FqrLtuxGqWFZrJrZEyOPy5lYr5dLBtgI3t1q4Waq4rPY9yEz39rrUd/N9bw88L9KkRsrlZzlc3tpOuWzY2TMON5ta7siDljs0NDSeB2i5IwcbDQvRzeN0kx55bPkRFon22g52+lLZemGMGtRqz0N76XK1jwhB2MaM45e+afmIctfrJlI61TF6bohf752WjahbZesGMSL0g66LhSiVbRgztGzXTQ+R2WrNROQqbDnnaOvtOgEWrTYb2eZQ43ApMhiVrR/FWJSRuVypmkhHVVy2LB+Lu+t1C1mA6hh9L8Ri6k7LRqQ4istK18X2AIIH2TaSuGyY/om4FItWW017KJe2H2HBbRSXQcTAZa3vIcpVcckYR3ZxWi53W85QLr0wRrZzlMuj10kUMyxiN0wfm0Ot1UxErioue054Ki73Ow4ymDwuReZYz+FyGnihb9JFqXRGtHjKY4OIhIlhJP/OtTUIragFaaw6hkGyrUEGic8wxjgGZe8zhtuKccGg4baUlREZZBzxTfE+ydYY1x/KfCgUsmOobY0BLrNjHP8eBmWcGIaB7zHOd1adg9Hn1kDbfEFxboUf4n3i1TzbopL3Eb4bg1waQ7iUjy1zlX8M6T0jbY9zmbxtlD/Hj1E0jn8PwzCwpYI8940cW1xrkg/SYUdyaRgj5qV0TdHA/YCmCi13aGhoaJwxtNyRg+vrTaSKorZVHtdND4sut3c6SLcGbZM6TtML0V76qNJDav/+Ug1prnhfEDG06m42LKTrn6w2IGEIW845apgrXRcLWDc3W5ABhA/yuGMHdDNdUHuw38VC5s8eVZFWimN4YYxHGq3WTKTHHy3XkOYK25hxtJDvtR0sYN1YbyJVHPQnsW2YPmq8b+90kEqreDe9kD5fS7hcqvSRjn4wwGVyjDBmqAPeatpI1z9dbSDtlv0RXFZ7Hrj8aquN1FXlT9cJsDj5cL8HyWmQy8NjXK7XMy6vLdchrYnPZUe4FAtYNzaakKdUc61p+ajxvrubx2Via/sRuHx82MfucB8s1SAZiPdFMUMd8HbThnzw2ZrM5XF+qj0Pi4Ffb7dRc66aBz0nRL384kEPMsl7OfPymsSlkBqurdQhYYhjyFzudzIuv9hoQVJR+dOyfCya393tYFE4j0uxoLhc7UMCk7mcCjjnz+x/3//+9/mTwAsjjN3g+Jgxxv0w5pxz7ocxZ4zl2sqfF0Qxj+LhtmIcxYyHUTyWbRwzHqS2XhgN9YcxNuBPPKY/4Ql9l/0ZZqu5PJk/w2xPy+VJz+1JuDztuT0Jl6c9t8Nsj3L5pOf2tCCiWzznPqflDg0NDY0zhpY7cqCfFq5uC9dPCx+01U8L108LJ9JPCz8VdCStoaHxPEBH0jmQaxtHjU9iK//wjWMr7Mc5xklsz6s/J/V93GNoLs+Oy+fhOpkEl9PAC32T/mStgeqOnzzMVn5/mo5rfQ8p8dfbbcgdP5Vsxfv6Xoj20cWDbOX3ncUqUnRhG0SM3kvTpo2GhScif7hch9whjsE5x3i/49Cd3S4REX2x2YLc8ROFP207oC/SioS7e12sov/04SEml7D1wpg+THfwW65mFQnvLWXVHcI2ZpzeSdP5nZaNJzR/utaAdKTism56aJe+tZOtoqu4NL2QPpG5TFPidx8d5zKMGb23VE25tPEU9msrdcgdsj9vp+lzpesiJf5ys4WKBBWXHTugG6nsdW+vC7nj7cXhXK7UsoqE9x/XIHcIWyZxudty0Mb/2XpW3aHyp256dDOVF27vdiB3qLi0/AhSzaNKHzLcu4+qSNF/KnEpZK/Npo2nsH+8WofcoTq3hz2Jy60WpCOV710noOup7DUOlx+kstdqzaK1lMsPHtcgd6i43Gs7eML35+tNyB0q3xumT1+mred3djtoglFxafsRfbyanNulw4zLn0lcTgPnSu4wDOM3iOj3iahIRP+Yc/57w+y13KGhofE84JmQOwzDKBLRPyKi3ySiXyKiv2YYxi9N85iVrotfQLGAIY+9MEbLdr3v4ddbZRvGDIsObTtAC7mIFGRbzjle77khfun3Ow4iRdUxnCBClFLre4jMVLZ+FCPCalo+okqVLWMckXbXCRDF7bUdRDfy+4Tvlh8hmq90XbS053KZRs91cziX0REuRbYzisu+l3F50HVHcikWuEZxGURsgEsRVY7isueEJ+JSRPOHvZNxKbKvUVx2TsilqMMfxaUbxANcDju3MpetMbjEdeKEqHfeazuQGFRc2ke4FNlgHpciq2uY/kguD3K4nGawe25u0kT0PyWidc75Juc8IKJ/TkS/Nc0D9tyQwjght5XuyiaP/YiR6SWTyPQj8tOTLduK3dyimCPdt/0IJ7ttB5hQ4n0x49jBzgtjclLbnhtSxAaPwTmndnrj8UNGVupPX/K9qfAnjDkmke1H5IXJ57adABNKHCNiHDcTJ4hxkXWdEBensGWM48bshTEusr4XUqTwZ4DL1NbyIvLD41yq/JF97zgZl00Vl0FMdiB8D8Cl7I/MpfDd9EJcyCp/wpgNnFsxD2Qum5Lvwh8nzOZBcm6HcynmQd+NcJNW+RPEjPpexqXK96aKyyAiNz23HSc4fm558rrg0klte0441B8/ihGUmF5mq5oHEZO5zOaaal7GXJqXYeZ7zw0pPsI750fnZcalah7I51ZcJ5Yf4cc6l0uc23iAy2nK0udG7jAM4y8R0W9wzv9m+u+/TkT/M875v3/E7odE9EMiou9973vf39nZeeq+amhoaEwSz4TcMS445z/inP+Ac/6D11577azd0dDQ0JgqztNN+oCIviv9+zvpaxoaGhovLM7TTfprIvpFwzB+zjCMGSL6q0T01hn7pKGhoXGmKJ21AwKc88gwjH+fiH5GSQneP+GcPzpjtzQ0NDTOFOfmJk1ExDl/m4jePms/NDQ0NM4LzpPcoaGhoaFxBPomraGhoXGOoW/SGhoaGucY+iatoaGhcY6hb9IaGhoa5xj6Jq2hoaFxjqFv0hoaGhrnGPomraGhoXGOoW/SGhoaGucY+iatoaGhcY5xbvaTPg0Mw2gQ0Wk3lH6ViJoTdOe84Xn+fvq7Pbt4nr/fk3y3P8E5V+69/EzfpJ8EhmHcyttk+3nA8/z99Hd7dvE8f79pfTctd2hoaGicY+ibtIaGhsY5xot8k/7RWTswZTzP309/t2cXz/P3m8p3e2E1aQ0NDY1nAS9yJK2hoaFx7qFv0hoaGhrnGC/kTdowjN8wDGPFMIx1wzB+96z9eRIYhvFdwzCuGYaxZBjGI8Mw/lb6+suGYbxvGMZa+v+XztrX08IwjKJhGHcNw/hJ+u+fMwzjZnr+/kX64OJnEoZhXDUM418ahrFsGMZjwzB+7Xk5d4Zh/O10Ti4ahvHPDMOYe5bPnWEY/8QwjLphGIvSa8pzZST4L9Pv+cAwjD972uO+cDdpwzCKRPSPiOg3ieiXiOivGYbxS2fr1RMhIqL/mHP+S0T0q0T076Xf53eJ6EPO+S8S0Yfpv59V/C0ieiz9++8T0T/knP8CEXWI6HfOxKvJ4PeJ6F3O+b9CRH+aku/5zJ87wzC+TUT/ARH9gHP+y5Q8XPqv0rN97v5rIvqNI6/lnavfJKJfTP/7IRH9wamPyjl/of4jol8jop9J//67RPR3z9qvCX6/PyaiP09EK0T0RvraG0S0cta+nfL7fCed/P86Ef2EiAxKurpKqvP5LP1HRFeIaIvSBXzp9Wf+3BHRt4loj4hepuSB1z8hor/wrJ87InqTiBZHnSsi+q+I6K+p7E763wsXSVM2eQT209eeeRiG8SYR/RkiuklE3+ScH6Z/qhLRN8/KryfEf0FEf4eIWPrvV4ioyzmP0n8/y+fv54ioQUT/n1TO+ceGYVyg5+Dccc4PiOg/J6JdIjokoh4R3abn59wJ5J2rid1nXsSb9HMJwzAuEtF/T0T/Iee8L/+NJz/lz1ytpWEY/yYR1Tnnt8/alymhRER/loj+gHP+Z4jIpiPSxjN87l4iot+i5IfoW0R0gY5LBc8VpnWuXsSb9AERfVf693fS155ZGIZRpuQG/U855/9D+nLNMIw30r+/QUT1s/LvCfCvEtH/xjCMbSL655RIHr9PRFcNwyilNs/y+dsnon3O+c303/+Skpv283Du/hwRbXHOG5zzkIj+B0rO5/Ny7gTyztXE7jMv4k36ayL6xXSVeYaSxYy3ztinU8MwDIOI/pCIHnPO/4H0p7eI6LfT8W9TolU/U+Cc/13O+Xc4529Scp4+4pz/20R0jYj+Umr2TH43IiLOeZWI9gzD+FPpS/8GES3Rc3DuKJE5ftUwjIV0jorv9lycOwl55+otIvobaZXHrxJRT5JFToazFuLPSPz/i0S0SkQbRPSfnrU/T/hd/ueUpFgPiOhe+t9fpES7/ZCI1ojoAyJ6+ax9fcLv+etE9JN0/PNE9BURrRPRf0dEs2ft3xN8r18holvp+fsfieil5+XcEdH/iYiWiWiRiP5bIpp9ls8dEf0zSvT1kJIs6HfyzhUlC9z/KL3HPKSkyuVUx9Vt4RoaGhrnGC+i3KGhoaHxzEDfpDU0NDTOMfRNWkNDQ+McQ9+kNTQ0NM4x9E1aQ0ND4xxD36Q1NBRIdxfcMgzj5fTfL6X/fvOMXdN4waBv0hoaCnDO9yjZuez30pd+j4h+xDnfPjOnNF5I6DppDY0cpO32t4nonxDRv0tEv8KTFmcNjaeG0mgTDY0XE5zz0DCM/z0RvUtE/yt9g9Y4C2i5Q0NjOH6TklbgXz5rRzReTOibtIZGDgzD+BVKHqDwq0T0t8VuZxoaTxP6Jq2hoUC6c9sfULI/9y4R/T8o2cReQ+OpQt+kNTTU+HeJaJdz/n767/83Ef1PDMP4X56hTxovIHR1h4aGhsY5ho6kNTQ0NM4x9E1aQ0ND4xxD36Q1NDQ0zjH0TVpDQ0PjHEPfpDU0NDTOMfRNWkNDQ+McQ9+kNTQ0NM4x/v9HDhDxsEFxlQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bar = Obstacle(Cuboid(vec(x=50, y=50), x=6, y=60), angular_velocity=0.05)\n",
    "v0 = StaggeredGrid(0, ZERO_GRADIENT, Box(x=100, y=100), x=100, y=100)\n",
    "plot(v0, bar.geometry, overlay='args')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define the simulation step consisting of fluid advection, bar rotation, and incompressibility."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit_compile\n",
    "def step(v, p, bar: Obstacle, dt=1.):\n",
    "    bar = bar.rotated(bar.angular_velocity * dt)\n",
    "    v = advect.mac_cormack(v, v, dt)\n",
    "    v, p = fluid.make_incompressible(v, bar, Solve(x0=p))\n",
    "    return v, p, bar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0c713cd3736a492da049b37cc991a446",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v_trj, p_trj, bar_trj = iterate(step, batch(time=100), v0, None, bar, range=trange)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's animate the x and y component of the velocity field separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x1affbacc580>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(dict(**v_trj.vector), bar_trj.geometry, overlay='args', animate='time')"
   ]
  }
 ],
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